Well, I went out this morning and got the turf tires mounted on the new rims just fine. A little bit of dish detergent and they popped right onto the rims with just a little bit of persuasion.
Now Jay is jacked up next to the barn and the left rear tire is off him. MAN ARE THOSE WET TIRES HEAVY COMPARED TO DRY ONES!
Problem is, the old bolts don't fit the new saddles! On my old rims, the square head of the bolt goes right inside the saddle and sticks out the other side, left- or right-hand depending on the offset you want.
On the new rims, the saddles are about as tall as the old, but much thinner, and they don't have a plate in the center, just four little "pimples" sticking out inside the saddle. I'm not sure if I need much longer bolts overall, or if I need slightly longer bolts with a very small square head that will still fit inside these pinched saddles?