Okay, here's where we're at:
As far as the rear derailleur goes, I got it working just fine shifting into and out of top and bottom gears. It's in the middle gears - between 4th and 5th, to be exact - that I'm still having an issue with lag. I'm starting to think that it might be the brand new SRAM 7-speed cassette that doesn't want to play well with the rest, but I'm still tinkering with it. If all else fails, I'll see about finding me a Shimano RD that works.
In the mean time, I can report that the original Sachs-Huret front derailleur is working just fine with the left brifter, so no issues there. The irony is that I have a vintage Shimano 600 FD on standby in anticipation of just this kind of issue, and yet it turns out that it's a rear derailleur that I should've ordered all along!