Dropped dramatically, but not entirely.  The underlying issue seems to be mislabeled antenna wires.  I’d made an earlier pass at trying this fix, but failed because I couldn’t find any of the other wires I was supposed to use in place of the one labeled “BT” that was attached to my bluetooth module.  Just now, however, with some more disassembly, I was able to find the other wires, swap the “BT” wire for the only other wire long enough to reach, and now my keyboard and mouse work from across the room.

Details:  Read this and this.  Open the case, remove all four SATA brackets/drives.  If you can see all four antenna wires, great, go for it!  (That is, swap the “BT” wire for the only other wire long enough to reach.  If you’ve got the Airport module, see those two links to figure out how to deal with those wires.)  If not, as it was for me, remove the heatsink cover (bottom-middle of case) and the front fan assembly (bottom-front of case), then poke around in the bundles of wire behind SATA bay 1, top of the motherboard/logic board, toward the front of the case.  That’s where I found the wires I needed.

To remove the heatsink cover, grip it at the edge closest to the motherboard and lift and pull toward you–it’s held in place by a few magnets, no latches or anything.

To remove the front fan assembly, unscrew the screw that goes through the motherboard at the top-right of the fan assembly and possibly look for a screw at the bottom-right of the assembly, just under where the heatsink cover was.  Once those two screws are removed, pull the assembly straight out of the case (perpendicular to the motherboard)–it slides in a track along the bottom of the case and pulls away from a plug on the motherboard (no cables to worry about).