I Love TTM (+ Prazi)!
I've completed it about 5-6 times now and no fish were stressed from it.
In fact when I TTM'd my tangs I would always have Nori waiting for them in the new tank and they love it!
I have tried Copper, testing both morning and night to ensure the therapeutic levels were maintained and I found this stressed the fish a lot more than TTM as they would refuse to eat for days, so I had to obviously stop treating, which means the clocks starts from 0 again.
It doesn't have to be complicated.
Also my main DT is ich free so I always use the tank water for TTM and treat it like a water change.
When you mention about cycled water, I treat TTM for 12 days and move to a QT with live rock and never had issues with ammonia.
I think you would have more of an issue with cycled QT and/or ammonia levels with copper since its not recommended to include Live Rock with Copper where treatment is recommended for +30 days.
Also there are a few users who have treated copper where ich has reappeared (eg.
ngoodermuth, and
Jeffdstafford) - could have been a mistake in the process (cross-contamination) but these copper treatments were documented regularly and still did not eliminate ich.
I think whats more barbaric is a good % of the reefing community who fail to QT their fish which leads to introducing ich/velvet and wiping out their whole livestock.
It is very common reading threads with the "I know I know I should've QT'ed but..."
After a few TTMs I feel like its a normal routine, like brushing teeth now

I feel TTM is easily manageable when your know your tank is ich free, its just like an extension to water changes.