Yeah, it was much easier than I thought it was going to be, too. Your "lift" sounds a lot like mine. I just use concrete blocks under each peg, then rock the bike back and forth and add pieces of 2x4 on top of the blocks until I get it up in the air. On the road, I carry an Eagle Mike's Quick Jack. It works good, but I've experimented with it and you have to be a lot more careful while wrenching on the bike. I'd use it if it was all I had, but if I had the option, would scrounge around the area for something else (rock, wood, etc.) to put under the bike to stabilize it while it's up on the Quick Jack.
If you want to continue to practice your tire-changing skills, you can do what I did over the Winter. I bought a cheap, Chinese "dirt bike/enduro" tire and wheel set off eBay for $20. Can't recall what size it is, but it's a good "in between" of the front and rear tires on the KLR. You can just keep it around and practice all you want, experiment with tools and patch kits, etc. For the price, you can't go wrong.