I can tell you how to do it, most of the ZT2800 and ZT3400 HST's are identical in servicing.
Remove the filter, oil will drain out-all of it will. That's how you drain them. It comes out fast too so be ready. Replace filters with new ones. Now, at the top, inside of the hst there's an allen head plug. Right in the middle, toward the top. 1/4" allen. If you have an allen socket, great use that if not use a standard allen wrench and pray for it. Clean out the hole where your socket will go in, and grab a cheater because those plugs weld themselves in, and will pop loose when you get enough torque on them, such that they're knuckle busters. There is a plug on each hst. BTW I have broken ratchets when the plug pops loose so you have been warned.
Now you're gonna fill the reservoir and let it continue to fill the hst until oil runs outta the hole u just took the plug out of. Repeat for the other side. It'll take roughly 5 quarts. Once both sides are full, and the plugs are back in, lower the machine to the ground, start the engine and go drive around for a while-to get it hot. Before doing so, make sure the oil level in the tank is about halfway up (which is actually over-full but trust me here). After you drive around a little bit go park the machine for the night, come out next day and look at the tank's oil level. You want it to be at the cold fill line. If it's over full, use a turkey baster to extract a little. If it's dry, add a little and watch the level-it will fluctuate with temperature and after a few mowing cycles it should stay roughly at the same cold level.
If you're doing it without any sort of lift I feel for you.
I have two tricks up my sleeve but won't go into those. It saves a ton of time but requires the "right touch" and secondly a special tool and fitting. Without them, takes about an hour & a half give or take, with them, 20 minutes tops assuming none of the bolts break off in the filter covers. And that's using a lift--without a lift, it's a half day project for most people.
I recently did mine, synthetic because I had it. One thing I noticed is that synthetic fluid expands and contracts a lot more and when the mower is cold the oil level is perfect (cold fill line) and after I mow, it's about 3/4 the way up in the tank. With the old dino oil, it rarely got much more than 1/3 of the way up. If you have a rough yard, and the oil level gets up that high, it can spew a little vapor out and it will make a mess as the dirt sticks to the vapors. Just warsh it once in a while, problem solved. Or use dino oil. It makes no difference. I noticed zero difference other than what I mentioned. It's not any quieter or noisier, no more or less power, not any more or less smooth, nothing. IF I didn't already have it, I would not have used it and just used some cheap kawachem 20w50 that I also had in a 2.5 gallon jug. Saved it for the engines since I am maintaining 3 diesel mowers and then my little gas burning ZG127S.