Best way to Audition amplifier?

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.  

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 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 

buterrier79

Most places I have spoken with do not allow a demo to be taken to my place for audition and the speakers I have are not widely available. What is best way to make the amp selection?

Under those circumstances, you should first work with the dealers that will allow you to demo an amp in your system.