What should I upgrade next?

You are going to get a number of different opinions in response to your question, but in a situation like yours I usually advise people to upgrade their speakers first. Some people will advise starting at the "front end" with a new preamp or better source components, but if the speaker is the choke point you won't hear the improvements upstream. The Maggie 1.6's are a fine speaker, and are sufficiently revealing that they will reveal later improvements in your other components. After you upgrade your speakers, I think your very nice change should be to the preamp -- the Adcom GTP-500II was, at best, only an adequate preamp (certainly not up to the standard set of Adcom's GFP-565), and there are many better preamps on the market now for a reasonable price.

I would replace the speakers. I have noticed a trend in the Audio magazines which have recommended systems, they often have $1000 - $2000 integrated amps driving speakers that cost $3000 - $5000. The speakers (and how they integrate into your room) are still the weakest link in the stereo chain. Maybe this says something about the quality of todays amplifiers too but, I stand by my recommendation.
I would change the wire last.

speakers. you might even take a years budget and buy some really good ones. you will never be able to detect the other chages in your system if the speakers cannot play it.

imo
Jim

I think you should buy a good turntable and some good records. Then, after you have improved the source, continue with upgrades down the chain, in the order of signal travel. I have heard some pretty low end speakers sound quite amazing when they are fed by a great front end. I have also heard some great speakers sound pretty crappy when fed by a poor front end. If you upgrade in the order of signal flow, you will achieve the best result. The source is the most important, as this is where the signal enters the system. At this time there is no better source than a good turntable. That is where you should start, if you are serious about better sound.