I was in the same position, as I have a single room for HT and 2 channel.
I started with a separate amp too, made an improvement, with my AVR as a pre in 2 channel. Still not satisfied, finally got a separate preamp for all 2 channel sources with an HT pass-thru when watching TV, and now 2 channel is substantially better.
If you want good 2 channel, don’t use your AVR. Either do as above, or perhaps an integrated as you mentioned, with an HT pass-thru if your room is dual purpose as mine is.
I started with a separate amp too, made an improvement, with my AVR as a pre in 2 channel. Still not satisfied, finally got a separate preamp for all 2 channel sources with an HT pass-thru when watching TV, and now 2 channel is substantially better.
If you want good 2 channel, don’t use your AVR. Either do as above, or perhaps an integrated as you mentioned, with an HT pass-thru if your room is dual purpose as mine is.