Near-field speaker placement

Yes, bass traps in a small room. Also small rooms are best served by speakers that don't attempt the lowest octave.

mesch, could you please briefly explain how can I identify this type of speakers? Sorry for the basic question, I guess...

Thank you!

The bottom octave is 20-40Hz, or to some 16-32Hz, frequency range. I was thinking of those speakers that have a -3dB down point just below 50Hz or -6dB below 40HZ.  Something in that range. Prevents excessive excitation of bass modes.  I get plenty of bass from speakers that fit this description in my 15'X12'X8' room. 

Do you know the roll off for the NHT Classic Twos?

Don't give up, given that your room is not square and LxWxH all differ you should find an acceptable placement. I have a headphone system however do not hear it as a replacement for a speaker based one. Please keep us informed as you progress.  

Thanks again, everyone, for your thoughts and advice. Right now, the best alignment I've found is placing the speakers along one of the long walls, 15 inches out, and 60 inches from the shorter side walls. I have bass traps in all four corners and 4-inch-thick acoustic panels on most of the rear wall. The speakers are 42 inches apart, with my listening chair equidistant.

My next rabbit hole involves my speakers (NHT Classic Twos). According to the manufacturer, the listener should sit 1.5 times the distance between the two speakers (50 inches between speakers = 75 inches from the tweeters to the listener's ears). In my current setup, an equilateral triangle is about the best I can do given the space constraints. I asked NHT about this and they said the Classic Twos "would hold up well in an equilateral triangle arrangement. The key is to have them pointed to the listening position. The drawback would be that off-axis dispersion would not be the best (i.e. there'll be a sweet spot) given the Classic Two's are two-way speakers."
My question(s): Is it worth chasing down a pair of speakers more suited to my room (13.6 by 9 by 7 feet high), i.e., a pair with a larger sweet spot, or a pair that might be engineered differently to perform better in a small room like this one? In this alignment the Classic Twos sound good at times, but not so much at others – specifically regarding piano, it seems. Maybe it's just me, but it just doesn't sound true. Anyway, I'd appreciate any advice on whether three-way speakers will improve (widen) the dispersion, and maybe any recommendations on more preferable speakers (in the ballpark of $1,500 a pair), bookshelf of maybe small towers. Gracias.

I don't believe a 3-way speaker will provide any advantage in dispersion over a 2-way speaker. There are many excellent 2-way speakers that provide a wide soundstage that can be had for $1500 (new or used). I use Esoteric MG-10s, 7 1/2" 2-way speaker in a room ~14 x 12'.  Soundstage extends beyond side walls with some recordings.