Sautéing big batch of onions
I have not personally tried this with onions, but whenever I need to cook large batches of something (for example, bacon) and I don't have enough space on top of the stove, I try to find a way to work it in the oven.

Although it's not going to be a true sautée, I think you could probably achieve what you want with a few sheet pans of onions (mixed with oil) in the oven.

This recipe would probably be a good guideline for time and temperature.  

If that doesn't sound like something you'd like to try, do you have a grill?  What if you laid out a large amount of foil across the grates of your grill (put a lip on the edge, basically make an impromptu baking sheet out of foil) and do them on the grill over low to medium heat until they're the texture you want?