Warping is from uneven drying, if the humidity is consistant and you dont have accumilation, you have nothing to fear from warping. The wood will never really rise above 20% internal humidity in room temp provided you don't have accumilation.... I would worry more about mold at that point.
If you are staining the stand... a uretane finish would be more than enough to seal the wood inside and out against humidity alone...
I would recommend Atleast using a waterproofing and mold resistant paint on the interior of the stand, for obvious reasons... no need to stain/urethane the inside if you paint it...
If you want it to hold water in the stand if it some how makes its way out of the sump than I'd use; the spray on rubber, epoxy, fiberglass resin, or silicone/paint combo, which will allow the inside of the stand to hold water, provided its enclosed to begin with(can't see your pics atm) ...
I'd rather have a leak in my water proof stand than making a hole in my carpet under my stand.