I have discovered two things to this point:
1) TASing with a mouse is a pain in the you-know-where;
2) this game lags horribly.
It appears possible that mouse movements might affect the RNG, which would make luck manipulation a very... interesting... task.
Anyway,
here's a rather rough WIP to demonstrate some of these concepts. I do a little bit of base setup and miraculously get a UFO to land almost immediately afterwards - I don't know what I did to do that, but a couple of previous attempts just had UFOs flying around; I suspect I moved the mouse a little bit differently to get that to work.
If nobody sees obvious flaws, I'll experiment with manipulating the battlefield into yielding a desirable outcome for a quick battle. Perhaps I'll do that anyway just to get a feel for it.
EDIT:
I've been playing a little bit with the battlefield yielded by the above movie, which seems like it will be good to continue the run: the UFO is a Medium Scout - the smallest possible UFO with a power source - and hence with the least number of aliens and the smallest - 40x40 - battlefield. Some exploration suggests there are 7-8 Sectoids, all but one of whom are in the UFO - the remaining one is within the line of sight of the starting position and he can be shot on the first turn. The UFO's along the same edge of the map but in the far corner, but having all of the Sectoids in one place should make up for that.
Most importantly, mouse movement does indeed affect the RNG. This means that luck manipulation is going to be an exceedingly finicky affair, but that it should be possible to come up with highly unlikely results.
600 or so rerecords later, I managed to
hit and kill the first Sectoid with one shot. This is with an Aimed Shot; trying to hit with a Snap Shot ate most of those rerecords, and an Auto Shot would waste too much time. I did hit with an Auto Shot relatively quickly, but I would rather not lose frames in that fashion; besides, hitting with one shot is that much more impressive when you're dealing with
red shirts.
EDIT2:
Look! I figured out how to
encode the WIP and put it up on DM!