Since better sound quality is the goal, I doubt seriously that anyone would hear a difference between the Denon X3500 and X3700, with or without external amps unless the Denon's internal amps don't provide enough power. This will only happen at VERY loud levels which few people seem to listen at frequently. Absolute worst case scenario, which probably wouldn't happen in the real world, is that your X3500 sends a signal to your external amp with .02% distortion. This would be up near reference level or higher, at which point your speakers are producing orders of magnitude more distortion of .5% or 2% or probably even 10% depending on frequency.
The X3700 is a great AVR, I'm just confident it won't *sound* different than the X3700 with *accurate* testing.
So, what WILL make a significant difference in sound quality? The speakers and subs. Here are your speakers, from this Stereophile review:
B&W 683S2 Stereophile Review
Off axis response looks equally colored.
I'd look at changing speakers if the goal is high fidelity sound quality. Sorry, I know that's a tough pill to swallow as B&W has a huge, loyal, long standing audiophile following.
A good pair of(non-retail brand, ID) subs will also add substantially to sound quality. Here, you can compare the B&W sub to SVS smallest, cheapest sealed sub that is now updated and improved, and also to a high end offering from Rythmik such as F18, E15 etc:
Data-bass subwoofer testing
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You can change AVR and amplifiers, for a few thousand dollars, but you will still 99.9% still be hearing your current speakers and sub. Actually closer to 99.95% since the difference in signal being sent to you speakers will be far less than .1%.