You're right about the lock-up TC improving economy but to be fair, the TC on the 760 is pretty tight in that respect, maybe later models had a lock-up but mine doesn't.
Simplicity on a budget? Hmmm, a few options but they're all going to be thirstier. Simplest of all is the B230E option but that's very little gain for a fair amount of effort. yes it will be an improvement but not enough to warrant the work and cost involved IMHO so not really worth it unless the engine came to you for very little cost. Even then i'd think twice.
If the sidelights are on, they don't go off with the ignition, only the main headlights. The day running lights go off with the ignition so first thing to check is the headlight switch, second is the interior light, if the switch was knocked or put in the wrong position, that would bring the interior light on, flattening the battery enough to stop it starting. Alternatively, one of the cells in the battery could have died.
Think you need to be more specific when you say "roll up cheap, low mileage, good condition 760's!" as it would be the V6 that would make the most improvement without resorting to a turbo which wouldn't necessarily give you the gains you need in bottom end torque etc.
*** EDIT ***
Just to tempt you a little more :
https://www.ebay.co.uk/itm/V6-METAL-...O/112943493951
Finishing touch for the tailgate when it's done!
