With hours of life wasted - it appears that the problem is this:
The Form I was instantiating was not initially displayed. It waited for a Windows event from an external process to then display. Because of this, no Form was ever visible at instantiation.
If instead of creating the Form at start-up and defer displaying it, I create the Form and display it off-screen at instantiation, everything magically works despite no other logic changes.
This feels like a bug in the .NET Framework somewhere. Best guess is a simple Control.Visible value getting cached somewhere that does not get updated when Control.Visible does, or something similar in Control.Load/Control.Show/etc. Or at a minimum, documentation missing from the MSDN.
I know if I provide Microsoft with a reproducible test case for this, they will say "you need enterprise level support to get us to look into this". And I know if I get my company to open a ticket about this, they will charge us thousands to come back with the response of "Have you seen this thread? This is how someone else worked around it" instead of actually fixing the underlying issue.
So hopefully I saved someone hours of their life should they encounter this.