Klipsch Forte ii too bright, or is it my room ?

I'd agree room would be first thing. Second could be wrap horn rather than change amp. I can only tell you the horn on my Klipschorn went from ringing like a bell to sounding like a damp rag. I tried everything from tiny to large amounts of various damping materials, no sense of natural timbre for me. Still, the damping could work for him if not as sensitive to timbre and tonal anomalies as myself. I still prefer tube amp vs ss amp on Klipsch Heritage, although I did have a little Musical Fidelity M2SI integrated ss in for a time that really wasn't too bad.

Also, how would you quantify which fix worked? First fix room, then speaker/rack location, then electronics.

If the room needs to be done anyhow then doing it 1st makes sense.

But if the speakers are new, then I would return them quickly.

While speaker placement is important, the speakers are also important.
And your list above does not even mention that the speakers might be a contributor..

The good part is that that list is also a long ways towards having a decent start at an Ishikawa diagram. And they are all valid causal mechanisms that can result in the observed problem.

He needs to change only one variable at a time, changing room first may allow him to live with rest of system. If he intends on keeping Klipsch (which do have some admirable qualities even in stock form), damping the horns could be a next possible solution, assuming he still has issues with  brightness after only room treatments. Still has issues, go to tube amp, I, and many others who own Klipsch prefer tubes as we have the similar tonality/timbre issues with most ss amps.
He could explore the first two options with practically no cash outlay. If resources of no concern, I'd suggest the room fixes with professional treatments together with tube amp as initial moves.
Purchasing new speakers first upsets the entire balance of what he presently has, like starting all over again from scratch. Keep the Klipsch and proceed in incremental steps.

Get a Chinese KT 88 integrated...roll in the Gold Lions and cover the floors. Reisong A20 is sweet and cheap. The Schiit EQ. will also tame them.

I owned Forte II's years ago.  The biggest issue I had with them was amp.  I used them with B&K and before that NAD. I was young and poor and didn't know any better. They were too bright.  Yet, I would love to have them back now.  I'm putting together a small cabin system and have a Jolida JD-1000a integrated amp and Spica TC-50 speakers which are not cutting it. The 1000a is a EL-34 tube based amp and I feel, it would be a perfect match for the Forte's. I currently looking for Heresy's or Forte's. Advise: Try out an EL-34 tube based amp.