Q:

How do you non-catastrophically reduce the mass of the Sun by half?

In my previous question, I asked how much mass the Sun would have to lose in order for Saturn's orbital velocity to be its escape velocity.
The answer proved to be somewhat unexpected - when the Sun loses about half of its mass, every planet will escape from the Sun's remaining gravity at about the same time.
So this is the promised follow-up question:
What plausible, believably feasible (not necessarily absolutely physically valid) method could be posited as a way for the Sun to lose 50% of its mass, without going through some catastrophic process?
Criteria and limitations:
A. Must occur within a millennium or two.
B. Should not involve intervention of some 'superior alien intelligence', but must be derived from some plausible natural event. (Somewhat lenient on this, but any alien intervention must be completely independent of the Solar System and not require any presence in the Solar System. That is, extraneous 'spooky action at a distance')
C. Must not create any phenomena that would have devastating consequences on life on the planets (i.e.: no radiation, excessive heat, energy surges) except for the diminishing of the Sun's current Solar contributions. The Sun just reduces in size, energy, and mass, but otherwise functions normally.
D. Once the planets are clear of the system, what happens to the sun thereafter is irrelevant.
E. The removed mass of the Sun must be done in such a way that the removed mass no longer contributes to the gravitational effects of the Sun.
F. The current position of the sun as the center of the Solar System can not be altered (Newton's Laws must be enforced).
G. The ejected mass can not itself become an alternative gravitational center sufficient to influence the planets, but must be dispersed into the galactic void. However, it is allowable for it to collect again and form a significant gravitational source somewhere else. The ejected mass does not necessarily need to reach escape velocity, but by some effect widely dispersed or otherwise relocated. 
H. It is allowable that, if the mass depletion occurs over time, the planetary orbits can correspondingly move away from the Sun until they reach escape velocity, with all attendant effects of doing so permitted.
Assume that the life on the planet is not dependent on energy from the Sun, but on independent locally sourced forms of energy. That is, life on the planet can be supported absent the Sun (No need for Solar light, heat, energy, gravity, or other Solar contributions). With that in mind, if any of these criteria are modified, then the modification must not effect the viability of life on or physical integrity of the planets, in any way. 
The method does not necessarily have to be under the control of any intelligent intervention, preferably not from any intervention from within the Solar System. Note, this is not a criteria.
Note this does NOT have a hard science tag. The effect can be caused by some as-yet-unknown but plausible scientific concept. 
EDIT
The Solar System does not absolutely have to be our solar system, but my planet-moon combo is based on Saturn or Jupiter. Humans are not a factor, and thus their intelligence and fate is inconsequential.
Another EDIT
Please also recall that, as the Sun loses mass, its gravity decreases and further mass loss will take less energy. That is, the remaining mass is not as tightly held as the starting mass. This fact may or may not be useful in your answer.
Clarification EDIT
Some may be thrown off by criteria C. The restriction on life is clarified by the later assumption stated after H. As long as the planets remain physically intact and maintain their integrity and general composition, criteria C is met. The planets have the same general structure, chemistry, and geological features.

A:

C. Must not create any phenomena that would have devastating consequences on life on the planets (i.e.: no radiation, excessive heat, energy surges) except for the diminishing of the Sun's current Solar contributions. The Sun just reduces in size, energy, and mass, but otherwise functions normally.

That is not possible, for three reasons.

About a third of the tidal influence on the Earth comes from the sun. Even if Earth would not escape, the tides would be changed globally, too fast to be nice on coastal ecossystems worldwide, which would all be f... Rough-loved. Other neighbouring ecossystems could follow in collapse.
The sun protects planets from interstellar radiation with its solar wind. The fact that Earth's rotation axis is kinda orthogonal to its orbit helps us survive solar flares, which always hit us perpendicularly. Once exposed to interstellar wind, we will all be f.. fried by crazy amounts of radiation coming towards the poles. We don't need to escape the sun for that to happen - merely moving the heliopause in can terminate us.
If a rocky planet surface does not depend on the sun to achieve a life-sustaining temperature, then either it is going through a hadean phase or it is excessively radioactive - neither situation would allow for complex life, maybe not even any life at all.

A:

Wormhole
[A,C,D,E,F,G] A traversalable wormhole would be an excellent mechanism to remove mass from the sun. A wormhole is consistent with general relativity while avoiding all of the pitfalls of violently moving mass from the center of the solar system (which could cause all kinds of orbital perturbations that would be chaotic or even fatal).
[B] Would you consider human construction natural? Perhaps humans build a wormhole. For convenience and efficiency they place it in the inner solar system (perhaps it requires a significant and constant stream of particles to remain stable so it's placed right next to the sun). Either by miscalculation or accident it falls into the sun. Unable to retrieve or destroy the wormhole it is left to silently eat away at the mass of the sun.

A:

There are a number of ways a star can lose mass, and I think it's worth talking about them:

A normal coronal mass ejection may contain $\sim10^{-18}M_{\odot}$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_{\odot}\text{ yr}^{-1}$, but this is not an expected event in Sun-like stars. 
Superflares are possible in Sun-like stars, although only in a very small population (1%), and likely would not remove as much mass.
The solar wind blows away mass at a rate of $\sim10^{-14}M_{\odot}\text{ yr}^{-1}$. Even the hottest O stars lose mass at $\sim10^{-5}$ or $10^{-7}M_{\odot}\text{ yr}^{-1}$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $\sim10^{-4}M_{\odot}\text{ yr}^{-1}$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch.
I do like LarsH's suggestion of bipolar jets. They've been observed in T Tauri stars, pre-main sequence stars that often evolve to become Sun-like. In other words, the Sun may have developed jets within the first ten million years or so of its life. However, I suppose it's really not going to happen anytime soon; T Tauri stars are very active, and have strong stellar winds that aid outbursts.

I think superflares are your best choice if you want the event to occur at the present stage of the star's life. If you are willing to have the star be very young, pick a T Tauri wind and bipolar jets, dramatically enhanced by some unknown factor. If you are willing to have the star be older and more evolved, a strong AGB wind might work.
Let's look at the timescales $\tau_{1/2}$ we'll need for the various processes, in order to lose $0.5M_{\odot}$:
$$
\begin{array}{|c|c|c|c|}\hline
\text{Process} & \text{Evolutionary stage} & \dot{M}\text{ }(M_{\odot}\text{ yr}^{-1}) & \tau_{1/2}\text{ }(\text{years})\\\hline
\text{T Tauri wind}^1 & \text{Pre-main sequence} & 10^{-7} & 5\times10^6\\\hline
\text{Superflares}^2 & \text{Main sequence} & 10^{-11} & 5\times10^{10}\\\hline
\text{G star wind} & \text{Main sequence} & 10^{-14} & 5\times10^{13}\\\hline
\text{O star wind}^3 & \text{Main sequence} & 10^{-5} & 5\times10^4\\\hline
\text{AGB wind}^4 & \text{Asymptotic giant branch} & 10^{-4} & 5\times10^{3}\\\hline
\end{array}
$$
1Lecture notes, Ohio State University

2Osten (2015)

3Cohen et al. (2011)

4Lecture notes, University of Bonn
Your best bet, overall, would be a system with an AGB star rapidly losing mass. Note that I give the time it would take for an O star to lose $0.5M_{\odot}$, but that would only be a small fraction of its total mass - not half. You'd need to extent that timescale by a factor of about 20 for it to lose half of its initial mass.

