It is not hard to "kit" the piston pump. What I found to be difficult was removing the bearing race from the suction end of the pump to replace the seal underneath the bearing cone. I finally ended up cutting the cone with hours of work with a die grinder. There just was no way I could figure to pop that thing out of there with any kind of a drift. But once I got the new seal and new bearing installed, my pump quit sucking in air and my oil quit frothing up.
I would take the pump off the tractor and carefully disassemble it, starting with the head bolts. Be careful not to drop and lose any of the small parts. After the head (pressure side) of the pump is off, I would next remove the bolts that hold the suction side together. Once that is apart, you should be able to inspect the wobble shaft and roller bearings that move the pump"s pistons. I would look for broken springs or obvious damaged bearings or where the bearing runs on the wobble shaft. Most of the small parts were included in the kit I got from this site.
Unless your pump has been sucking air, you probably do not need to replace the suction side seal or the bearing and cone it rides on. I would sure try just doing the kit before I went to the considerable hassle of changing that bearing and cone.
I have had some problems with a gasket blowing in the pressure side of my pump. It would always blow in the same place, where the gasket is very thin. I always knew when that gasket blew, because oil would leak heavily out the side of the pump. After changing that gasket a number of times, I wondered if it would be possible to get a better gasket. I couldn"t find any, so I decided to MAKE a gasket out of polycarbonate. It probably took me 6 or 8 hours to fashion the much stronger gasket and make it fit exactly. But so far, after about 8 hours of operation, the pump is not leaking again.
I sure like your idea of adding a barbed fitting and a plastic tube to recirculate the oil while bleeding the pump. I have always just opened the pipe plug on the pressure side and let it run on the ground until the bubbles quit. Kind of messy. Good luck!