On a LP that I use mainly for standard, will dropping it to D-Standard for a few days at a time (and doing this fairly regularly) warp the neck? I always played between standard and a half step down on my Martin, but that's a whole different ball game.

Also, would beefy slinky strings work okay for these tunnings? I usually play power slinkys but I still have some excessive buzz when playing hard... After months of trouble shooting the only real possible reason left is that the neck doesn't have a lot of relief (truss rod zeroed out, I got about 8 hundredths relief). Action is decently high too.
No, it won't warp your neck. As always, check the truss rod occasionally to see if it needs adjustment.

The key is setup, the gauge is obviously a factor but D standard is close enough to E that once set up properly you should be able to switch between them with few or no issues. A super straight truss rod might be contributing to the buzz, although it would be smart to have someone check the frets to see if they need a level/crown/polish too. A little buzz is ok if it doesn't come through the amp.
Nope, it won't warp the neck and yep, those strings should be fine. I go from E standard to 'totla mad' tuning (A♯, G, C, F, A, D) on my Explorer (because I'm that cool) with a D'Addario 11-56 set, so you should be absolutely fine

Charvel DX-1 FR / DS-1 ST / DC-1 FR / Custom Strat / La Patrie Hybrid CW / Vypyr 30 / VK100 / 1960A