After I commented on the question I started wondering what an observer inside a collapsing shell would experience.
If you construct a spherical shell then an observer inside it feels no gravity. This is true in Newtonian gravity, and is also true in General Relativity as a consequence of <PERSON>'s theorem i.e. the metric inside the shell is the <PERSON> metric.
In principle we can take the shell and compress it until it's external radius falls below the Schwarzschild radius $r = 2GM/c^2$, at which point the shell will start collapsing inwards and form a singularity in a finite time. In fact it's a very short time indeed. Calculating the lapsed time to fall from the horizon to the singularity of an existing black hole is a standard exercise in GR, and the result is:
$$ \tau \approx 6.57 \frac{M}{M_{Sun}} \mu s $$
That is, for a black hole of 10 solar masses the fall takes 65.7 microseconds! I would have to indulge in some head scratching to work out if the same time would be measured by an observer riding on the collapsing shell, but if the time isn't the same it will be of a similar order of magnitude. This means much of the question doesn't apply, since the shell cannot be stable long enough for the black hole to evaporate. 43
However it leaves open the interesting question of what the observer inside the shell experiences.
Curious as it seems, <PERSON>'s theorem implies the observer experiences absolutely nothing until the collapsing shell hits them and sweeps them, along with the shell, to an untimely end (a few microseconds later!).
Response to comment: time dilation
The infall time I calculated above is the proper time, that is the time measured by the freely falling observer on their wristwatch. You need to tread carefully when talking about time in relativity, but the proper time is usually easy to understand.
Re time dilation: again we need to be careful to define exactly what we mean. In the context of black holes we usually take an observer far from the black hole (strictly speaking at an infinite distance) as a reference and compare their clock to a clock near the black hole. By time dilation we mean that the observer at infinity sees the clock near the black hole running slowly.
A clock in a gravitational potential well runs slowly compared to the clock at infinity. This was discussed in http://physics.stackexchange.com/questions/69043/the-higher-you-go-the-slower-is-ageing/69048 (and also in http://physics.stackexchange.com/questions/10089/gravitational-time-dilation-at-the-earths-center). It's important to understand that it's the potential that matters, not the gravitational acceleration, so even though the observer inside the shell feels no gravitational acceleration they are still time dilated compared to the observer at infinity.
Note that the time dilation relative to the observer at infinity goes to infinity at the event horizon, so it makes no sense to compare times inside the event horizon to anything outside. 43