Putting the filter into a different position shouldn't cause you any issues. Having it upside down (hole side down), may create the situation you are trying to avoid, though. I take it your overall goal is to ensure the oil filter remains full of oil even when the engine is off, so upon startup the engine doesn't have to "refill" the filter. One of the problems with what you are planning is the filter will drain back down the oil lines when the engine is at rest. It will have to refill every time you start the engine. If the oil filter is the type which has an anti-drainback valve, the oil will remain, but it will create a huge mess when you take the filter off. This will be no better than what you deal with now and may be a lot worse. The anti-drainback valve will most likely keep the filter from draining back into the sump even if you do puncture a hole in the filter.
My suggestion to you is to relocate the filter, yet place in in the down position and not tempt fate. You'll be able to pull the filter off with minimal fuss/mess and then drain it as usual in the drain pan. Easier access to the filter itself is a good goal, especially since you won't have to take the skid plate off to change it.
One of the great things about a filter relocation unit which you may or may not realize is, with them, you don't have to stick with the OEM filter for the vehicle. Many times a larger filter is fit for the relocation unit, which provides added engine protection with the ability to clean the oil better in the long run. These replacement filters are usually quite a bit more common than OEM, which makes them cheaper as well. Win/win, in my book.