Will Klipsch Forte IV's Work In A Smaller Room?

Just buy the best 5 watt tube amplifier you can find.  You won't need more. :-)

Seriously, though, you might want to shop for vintage tube gear from the late 40's and early 50's to go with the speakers (assuming they are in good shape or have been recapped).  

• The advantage of those horn speakers is the instantaneous dynamic range they can reproduce....but you won't need power to get that affect.

I have owned many Klipsch speakers including Heresy, Quartets, Chorus, and CF-3 (my favorites. My room is larger, but my actual available listening space is near the dimensions you indicated.

I'm assuming 12 X 5 is a typo and that it's 12 X 15. I've also had Kef Reference 1, Harbeth Compact 7, Super HL5, Evolution Acoustics Micro Ones, and Gershman Acoustics Studio Xdb (all smaller monitor type speakers) and they all sounded better, imaged better, created a more expansive soundstage and were easier to listen to than any of the Klipsch.

I'm not saying the Fortes will sound bad in a small space. With your set amps and at low volume listening to acoustic music, they might sound magical.

In my opinion and experience, even Heresy are too much for a small space unless you like acoustic stringed instruments at low volume or want to damage your hearing. They're great for either of those types of listening, but if your tastes lie elsewhere, you'll probably be better off changing amps and getting smaller speakers. 

8wpc - very limited high sensitivity speaker options within budget.  Likely Klipsch is best option, then try to get it to work with the room the best you can.

Agree Razz would be a significant step up. 

You could make it work at midfield distances.

If you are set up on the long wall of 12.5 ft,

Pull them 1 ft from front wall and leave around 4.5 feet behind seat and back wall. Such a listening position would position the listener out of some some problematic lengthwise modes in the room. It would imply a 7 feet midfield listening distance from the speakers, which is enough distance for the drivers to sum properly. Corner loading is a hindrance to perceivable resolution. Hence, don't put the Klipsches on the corners and set them up 6 feet apart, resulting in a 6-7-7 isosceles triangle.

Place a sub each on each sidewall behind your seat to address widthwise nulls. The subs can be good performance micro subs like the kef kc62 for the small room.

Play with toe-in until you get a good amount of envelopment working with the space behind you. 

I bought my kid a pair of bookshelves, 2 ways with a 6.5” woofer and in his 9x11’ room bass was overwhelming. Was it flat?, neutral? Nope, was it fun h e l l yes.