Some thoughts, mostly based on experience -
"a dirt area (on a mild slope)" - when you're dealing with heavy and/or awkward things on dirt, there's no such thing as a "mild" slope

- BTDT - I would find/get a piece of scrap plywood at least 3/4" thick and a few 2x4's and make a LEVEL "runway" for your floor jack if at all possible.
"they both come down at once." - True - sometimes gravity CAN be useful :laughing:
" I just see putting it back together as a real PITA. " - Maybe, but if the trunnions/sockets on your cylinders are like mine, it might be easier than you think. It's possible that the sockets on that bottom plate are deep enough to keep both cyl's fairly well aligned while you jack the plate/cyl's back up into position, with just some minor guiding to line up bolt holes and upper trunnion sockets.
"I'd rather just drop it off to someone who does that for a living" - If you're going that route, I would DEFINITELY recommend dropping the whole shebang, taking the ENTIRE cylinders in, and having them REASSEMBLE for you. I can tell you firsthand, that even with the necessity of a come-along and a good external anchor point, those "guts" will come OUT much easier than they will go back IN

- It's not a lot different than trying to install new pistons and rings in a newly bored out engine WITHOUT a real ring compresser and some experience...
Also - looking at your earlier pic, it appears that if the cyl's were resting on the plate with their LOWER trunnions sitting in the lower sockets, then the 4 studs that bottom plate attaches with, look to be long enough to start them into the holes in the plate BEFORE the upper trunnions would need to line up with their (upper) sockets -
If so, I would take the (rebuilt) cylinders (separately) and BALANCE them (by pushing the rod in a little bit at a time) til they will balance
ON THEIR OWN on their lower trunnion - that way, you should be able to set them in their respective sockets (on the lower plate) - then, pick up that plate/cyl's and balance the ENTIRE thing on your floor jack (better if the jack can be raised just enough so it doesn't tilt the "load" by interfering with the jack's frame) - By balancing each cylinder
FIRST, you will probably generate less "blue air" putting things back together since you'll have fewer things fighting you...
Next, (assuming you are working on your LEVEL scrap plywood) you should be able to roll the whole thing under the hoe and start lining up studs to holes - once it's raised
just high enough to start into the stud holes, you can hopefully align the upper trunnions with their respective sockets - I've been known to hold two things in place while laying on my side and using my FEET to operate the floor jack, sounds like that might work for you unless you can conscript a HELPER
If you measure everything before you start, you may find that it's necessary to raise the hoe on the stabilizers and block it in place SOLIDLY - otherwise you may not have enough vertical room to manipulate the jack, plate, and cylinders without hitting the studs - (another comment from "blue air country"

)
That's about all I have - hopefully a couple of these points will help the job go smoother for you - Oh, and you also might be able to get your money back on that pipe wrench :thumbsup: ...Steve