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

First things first.
Fix the room before doing anything else.
It's like building a house and making the foundation later on.

It may mean more than just adding curtains.
Place a rug on the tile floor. Wood and tile floors look great with a nicely matching rug (rug shops let you try several rugs for free for a few days before buying).

Why do I say this? Because you will learn so much about how to deal with room acoustics.
It’s also fascinating how some changes seem to make a huge difference and how some are very subtle.

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

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.