Noticed you have a 95 Continental. I had one that I overhauled for my son to drive; we enjoyed it then sold it. Black with red leather interior, base model. Nothing else drives like a Lincoln for the money especially the 95-96 Continentals/Mark VIII.
As for your parasitic load, the Riv has a high parasitic load. These are difficult to find but I hate when people just guess... has anyone used a meter to check circuits at the fuse panels to find out which circuit is passing the load? If not then say so and I will comment more on that.
Thinking out loud -- seems that every one of these electrical gremlins have been different in my troubleshooting on my GM cars of this era. One time it turned out the problem was leaving a phone charger plugged in, with no phone on it, while the car was parked. NEVER do that. Another time it turned out the MALL (Riv's body computer) had been shorted while I was puttering around with something else, and had to be replaced. It did not fail when shorted (I blew a fuse) but it started doing stupid stuff (it controls the seats, the seat/mirror memory, and such).
By far the most difficult troubleshooting turned out to be an on-again-off-again short in the underseat wiring. SOMETIMES a wire with chafed insulation would short to ground but it was not a dead short, so it would drain the battery through the seat control circuit. That one was found by smell (where is that hot phenolic smell coming from?) then feeling the wiring for heat. Tedious. Hit paydirt when I got to the thermal fuses under the rear seat, took a while... while the car's off - pull the seat and check them, they are little silver fuse-shaped cans, I think 4 or so of them. they should NOT be warm at all. However if one is warm/hot it is likely to be associated with the problem circuit. There are other circuits with thermal breakers at other fuse panels in the car.
Point is you can find the problem by starting at the panels and measuring, and I was wondering if you'd done that.