What technique should I use to make latkes for a party so that I don't have to stay in the kitchen?
Number 3 will give you the best results. There simply is nothing as great in this world as a latke crisp from the frying pan, having spent but a couple seconds on a paper towel receiving the blessing of a few flakes of good sea salt.

I've never tried number 2. If you do, please report back.

Number 1 will not give you crisp latkes. They will still have the delicious taste of homemade latkes, but they will be soft, not crunchy.