Best way to Audition amplifier?

you can buy many xlnt amps with a 14 or 30 day trial period

I suggest you try the Benchmark amp (see their web site), as well as the new PS Audio (in mid-April) and maybe Audio Alchemy, nad Masters and others at mail order dealers like Music Direct, Audio Advisor, etc.

you need to overcome confirmation bias so use double-blind testing for both extended listening and rapid A/B switching 

Not naming the loudspeakers you have or the amps you are considering is a good way to limit the usefulness of the responses.

You can bring your speakers to the dealer.  Just as an aside, you are assuming that a new amp will give you the improvements you seek.  That may or may not be true.