Edit: Pressed last night and got 13 gallons which I thought was pretty good but it was a mess. With a mesh bag in the press the sediment clogged the pores almost immediately so I placed a second bag on the bucket and let the, whatever you call it, peach pulp fill the second bag to about 1/4 full then hand rang it out to the consistence of a modeling clay. When done out of 100 lbs of peaches I might of had the bottom of a bucket filled 2" of pulp. I was a pain and took around 4 hours. I surely hope this turns out to be worthwhile.
I have had similar messes with fruit wines in the past. Best I've done so far is using various sizes of hardware cloth (mesh screen) as a progressive filter. Starting with the most course, placed on top of a target bucket, dump the must through, catching the biggest chunks, put the chunks in a mesh bag. Continued with 3 progressively smaller screens and ended up with a bag of goo to squeeze the juice out of. Put the wine in carboys and racked it off of the sediment a few days later. Makes you appreciate the ease of pressing grapes....................