My thanks to Bill Vojak and Laird P. Broadfield. Between them I got enough information to get the job done last night. I'll probably test fire the new configuration this weekend, but all seems well.
The new trigger makes a small but significant difference. As near as I can tell, it's just a thinner version of the original, without grooves. All other angles and sizes appear to be the same. It is a little more comfortable for my hand. YMMV.
Mr. Moderator: Perhaps this belongs in the archive? It may come up again and I probably won't save it forever.
The details (left, right, up and down are relative to normal grip):
It should go without saying, but I'll say it anyway: Nothing needs to be forced in this procedure, nor are any parts damaged or replaced. If you bend or break something, you screwed up. Be particularly careful of fine wire springs and such. SIG will likely charge you big bucks to replace them.
If you're not comfortable with tools and mechanical stuff let a gunsmith, preferably a SIG armorer, do this for you. For an expert the whole procedure should take less than five minutes.
NOTE: There's a spring on the left side that normally fits into detents in the left of the slide stop pin. It will have to be moved out of the way to completely remove the pin. This will take some fiddling, but requires no special tools. You have to position the right side of the pin and wiggle it appropriately. Don't try to drive it out once it's disengaged from the right side of the frame (you can't). Sorry, I can't describe it better than that.
NOTE: The trigger pivot pin has two grooves in it that fit into slots in the slide stop block. There are two possible ways the pin will fit. Only one is correct. The slots must be facing diagonally down towards the front of the frame. Use a small screwdriver to adjust the pin as you replace the slide stop block. Tilting the gun on its left side will help keep the slide release lever out of the way while you do this. (Remember, it pivots on the same pin).
NOTE: The take down lever pin has a cut out on its far right face that fits over the spring. You can then move the spring out of the way by twisting the lever. Why they didn't put an equivalent cutout on the inside right surface I don't know. It seems obvious and would make disassembly somewhat easier.
That's it. Good luck and thanks again to Bill and Laird. Once again, the internet came through.
FWIW, I have a couple of suggestions. I had the most difficultly with step 4. After fiddling with the take down lever and spring for a while, I figured out that if you pull gently on the take down lever while turning it counter-clockwise, the lever pushes the spring out of the way for you (similar to how the notch aids you in reassembly). This method also helps out in reassembly after the far side (right side) of the lever has passed the spring. This made it as easy as pie to remove and install. Secondly, after field stripping, the hammer remains cocked, and therefore prevents the slide stop block from coming out. It might be worth mentioning to decock the hammer before starting.