DTS HD and TrueHD use a combination of HDMI connections and a bluray disc that uses those lossless codecs; if you have a player that handles the decoding you don't even need such in your avr really (as long as you have the connectivity to take advantage of the player's processing). Calibration is somewhat a separate subject, not sure if you're connecting them.
Not really as far as having REW help with the eq, was just putting that out there as an idea, not really thinking of your budget at that moment. You can see what you're hearing with such so to speak, but to implement the eq solutions that REW can come up with need to be implemented with other dsp than the typical avr provides (or provides access to).
You can perhaps implement the most important eq typically, that for your sub, depending what dsp you're using for eq'g the sub. The
iNuke DSP series can accept such, or a minidsp unit
https://www.minidsp.com/applications/auto-eq-with-rew
DIY and use of measurement mic and REW is a good combination for the long haul; perhaps with your current budget a simple avr will be fine for now but think about it for the future. Audyssey in my opinion will do the best job of the major basic avr auto eq programs (YPAO or MCACC) to eq your sub; not 2EQ but any MultEQ version
http://www.audyssey.com/technologies/multeq/flavors
Are those first two Yamahas and the third an Onkyo?