Question: I've been reading through other posts about such megastructures and they're getting me part of the way to my destination. Wanted to see about a few specific options my imagination has latched onto.

The original concept is a tower, an arcology with a 1 km base level (willing to taper it as it gets higher if necessary), reaching to at least 8 km altitude. 

Assume that available power is not an issue.

One idea is: Blocks, rectangular or triangular prisms, containing powerful electromagnets that are the 'mortar'. I liked this option because the society is ancient, and a blocky look fits the aesthetic better, masking the futurism. I realize it is power inefficient. Would such a thing work on this scale?

Thanks!

EDIT to reflect excellent comments: 

Trying to avoid elegant solutions such as Space Fountain, Space Elevator, etc. We want to solve the issue of structural stability with brute force as much as possible. Would a system like this hold up versus gravity, bending and torque at high altitudes?

Answer: 
Easy peasy. Basically, you want lucid dreaming with an I/O interface.

(Note: If I can dodge work enough I will try to find the New Scientist sources for this to add to the answer later, but I have read articles on all these three points recently)

You simply need to rig up a brain interface into the optic nerve. There is recent technology that can show a grainy but identifiable image of what someone is looking at simply by measuring brain waves; that gives you the output part. 

The input part you'll have to handwave, but it's not too much of a stretch to come up with something that can trigger specific images.

As for the immobile part, that's exactly what the body does naturally during REM dream sleep. So simply plug in your I/O helmet, trigger the body's natural REM state to immobilise your muscles, boot up the lucid dream for the world you want, and voila!

This addresses the comments I've seen here a few times - about the difficulty of immobilising muscles, and about fast/fine control; I have incredibly vivid, occasionally lucid and almost always sci-fi dystopian dreams, and I can confirm that I can walk, run, jump, fly, fight, drive vehicles, fly planes etc etc etc and all without falling out of bed, and I'm pretty sure everyone else here can too :)
[Functional MRI](https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging) allows noninvasive measurement and characterization of brain activity. With high resolution one could map and characterize brain activity corresponding to various voluntary activities. This is not science fiction; described here (in 2012) is a device that uses brain fMRI to generate letters and spell words.
<https://www.sciencedirect.com/science/article/pii/S0960982212005751>

So controlling something with your mind noninvasively: yes.

What about feedback directly to your brain. This could be accomplished with [transcranial magnetic stimulation](https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation). Magnetic fields are used to produce current in a nerve, replicating the effect of that nerve firing. I googled to see if this technique had ever produced hallucinations in a person (as one would expect if a sensory nerve were stimulated in absence of inputs from the sensory organ). These folks propose that ball lightning is a product of exactly this phenomenon, occurring naturally. !
<https://www.technologyreview.com/s/418887/magnetically-induced-hallucinations-explain-ball-lightning-say-physicists/>

So efferent and afferent nerve control is possible with near future precise magnetic technology.

The problem then is moving the remote without moving your body. That can be accomplished with mid 1900s technology. Paralytics are routinely used to prevent muscular motion in persons on a ventilator because of illness or surgery. <https://en.wikipedia.org/wiki/Neuromuscular-blocking_drug>
It is upsetting to be paralyzed while not sedated as occasionally happens by accident. You can be paralyzed, awake, and feel pain. For purposes of the scenario in the OP I think paralytics (and respiratory support with a ventilator - you are paralyzed!) would serve.