Speaker recomendation

Was in your position precisely and bought the Tekton Double Impacts. They are perfect for your room size, will work with your budget, and, easily, have enough volume and dynamic range.
If you research these, pay attention to DI speaker owners, not disconnected responses. You will note that all real owners of the speaker praise it wholeheartedly.
Eric Alexander, the owner, is fine to deal with if you are straightforward. Make him promise to send you the grills if these are needed.

OP - Where did you get the idea that the Golden Ear References are better for rock than other types of music?  I have heard the model Ones and found them to sound quite good with a wide array of musical types.

The GoldenEar Reference has some flaws in the upper treble, and integrated subs are almost never a good idea.

1) Get drapes/curtains. Room treatment in general would be very benefifical, $750 goes a long way, Acoustimac is a good site, I’d get a lot of their 48”x24”x2” panels (or short/narrower, but you want the same thickness).

2) Probably Salk SoundScape 7F for the speakers, or the Ascend Acoustics Sierra Tower with RAAL upgrade for 90% the quality at 50% the price ($3K vs $6K).

3) Get dual subs, that room is very large, even in close proximity the bass will be too low. Dual Rythmik F15HP’s would run you $2400, they have very low distortion and are very fast. If you want them in a custom finish, Salk buys the drivers/amp from Rythmik, but makes a better cabinet (thicker and more bracing), and you can get them in whatever finish you want (if getting the Salk speakers, you can get them to be perfectly matched), dual of these would run you $3600 plus shipping.

4) PSAudio’s Stellar Gain Cell DAC and S300 Amplifier combo for $2700 ($3200 if purchased separately). An excellent DAC/preamp and an excellent amp.

5) If you are tech savvy, I would recommend $300 for a MiniDSP 2x4HD with mic, which would allow you to DSP correct the speakers and subs. If you are not tech savvy, no big deal.