… but an amp is about the only thing that seems reasonable
High-end audio is a small niche market above box store offerings, and can get very expensively “unreasonably” quickly. For Sonics, the entire audio chain matters: including source(streamer+DAC), preamplifier, amplifier, speakers, and cabling.
While the OP seems to have a great surround system, simply switching from the internal Integra amp to an external amp will have limited effect as the rest of the audio chain will likely limit Sonics. Usually it’s much better to split surround and 2channel audiophile systems as it’s extremely difficult to lift 2 channel Sonics to satisfying levels.
So to answer the OP’s question a better amp would likely be sonically better, but trying to squeeze great 2 channel sonics from a surround system is extremely difficult as better 2 channel components simply perform better.