Replaced the blades yesterday; everything went smoothly. You all were a big help--thanks! I figure I'll put an epilogue here, since half the things I read on this forum are archived threads.
Bought a 1-11/16" socket, an 18" slider bar (much cheaper than a ratchet) an 8" extender bar (to get me clear of the tail wheel), and a 3-foot length of 1" iron pipe. I soaked the nuts with WD-40 and let it sit for an hour or so. Then I took my new wrench and cheater pipe and broke the nuts free. Left them finger tight, though.
Rousted a nephew away from the basketball tournament and into service. Levered the cutter up in the air with a digging bar, and nephew slipped in four jack stands. Then I kicked the cutter as hard as I could from the side, and thought about how I'd feel about being underneath the cutter right then. It didn't budge visibly, so we proceeded. We did one blade at a time. Nephew loosened the nut the rest of the way, while I caught all the parts that fell. Then I took put the new blade and washer on the bolt and pushed the assembly into place from underneath while nephew tightened the nut enough to hold. When both blades were on, we levered the cutter back down on the ground. Chocked the tail wheel so it didn't roll. Now to tighten the nuts.
There's about 200 lbs of me and about 100 lbs of nephew. We were pulling about 3 feet from the bolt, so we'd need 150 lbs of force. The landscape rake weighs 160; we lifted it up in the air so we'd know what the right force felt like. (Answer: pulling for all we're worth.) Then we did that.
Two observations: 1. When I put the blades back on, my chest was under a piece of steel that would make a fair guillotine blade. Didn't like that much, but I couldn't see any other way to make sure the keys were in the keyways and the blades had the right play in them. 2. You can almost always get a 12-year-old boy interested in things involving really big wrenches.