Get a nice 50cc saw, put a 20" bar and some skip tooth chain on it and go cut up your trees. You'll only have a few 20" rounds from each tree and then they will begin to get smaller. In 45 minutes you'll be done, if you don't hit dirt and dull your chain, and you'll have the saw that fits your purpose going forward. Don't buy a bigger saw than you want for one job!
If I'm going out to cut 20" hardwood I would probably take my 562, but if I'm out cutting with my 550 and find that I need to cut up a 20" tree, I just cut it up with the 550. I have any number of bigger saws back at the shop, but it just isn't worth it to go back and get one of them to do up one or two trees.