Some interesting comments here on mower deck R&R.
The plywood-on-casters platform is something I've had around for maybe 50 years, and I don't recall where it came from. Chuck's suggestion of the 3-caster dollies might work a little better. And I think it interesting that Deere put round positioning holders on later decks so that you can roll the deck out on the anti-scalp wheels.
On the M01013 50" decks, I take all four anti-scalp wheels off the deck and back off the stop to allow the deck to drop all the way down.
Remove the belt from the PTO pulley, lift the deck all the way up, roll the platform under it, and drop the deck so that the links are loose.
Disconnect the rear links and remove them from the tractor, pull the J-pins with a bar, remove the mule drive, turn the steering, and roll the deck out. Installation is the reverse. A good yank on the front of the deck will usually get the J-pins to snap into place.
If I had to do this on the ground rather than on a concrete floor, I'd just use a couple of chunks of 2X4 long enough to slide the deck out on them, rather than trying to drag it on the ground. Might need 4X4 to hold the deck high enough to hold the links loose for R&R.
As a side note, the draft arm that is welded to the cross bar that was originally installed tends to break at the cross bar. The current Deere replacement has a reinforcement welded in there, but you have to install the piece upside-down because they put the reinforcement on the wrong side. No real problem, as you can swap sides with the two lift links coming down from the tractor. Also, when reinstalling the two lift links, make sure the bellcranks on the tractor are flipped forward.