If you are planning to start tinkering with ARs, get some tools. What you are proposing would take me about 45 minutes. As far as the headspace goes, I do a quick check using "go" and "field" gauges, but I've never seen a barrel, from a reputable dealer, that had head space issues. Whether you're going to NEED a new bolt depends on how worn your bolt is.
I'm running an 18" barrel with a rifle length gas system and a heavy carbine buffer and haven't had any problems. If anything, I will shoot very smoothly, if you stick with the carbine length recoil system. Since you're going with a 20" barrel with a longer dwell time, there's less chance of your having problems.
Whatever you do, be sure that you get a good fixture to clamp your upper into a vice when you work on the barrel. Don't try to improvise on this. ARs are tough, but they are still made of aluminum and it's easier to tweak them than you may think.