Does anyone have suggestions for an integrated that meets the OP’s requirements but instead of HT bypass has internal preamp bypass (preamp in) so can use integrated amplifier section as the LR amp for HT purposes controlled by AV pre? This should theoretically improve the overall sound for multichannel TV and movies by releasing AV of LR power duties - assuming the amp section of integrated is powerful enough and of higher quality than AV. At the OP’s suggested bugdet - assuming that is likely. AV DSP should level volumes in any case.
Asking because just yesterday I thought about making this same move.
kn