Well, although I am new to the organization of a mock trial invitational, I do know that an incredibly invaluable asset to a tournament is for coaches to be able to see their teams compete so they can do what they're supposed to do, and coach their own teams. Seeing your team in competition is a better representation for what they need help with than any scrimmage or practice ever will be. If you can do a good enough job recruiting judges there's less of a chance you'll have to ask coaches to judge.
If you can find the money to pay for the tournament elsewhere, you can offer what ASU can, and have a tournament without registration fees. Your best bet for this amount of help would be law firms, restaurants, and hotels who can benefit from you directing business their way during the tournament. Princeton Review has sponsored quite a few tournaments in the past, but now they seem to only be helping with the regular and post season(Regionals, Opening Round Championships, and Nationals), at least this is what I've been told.
Also, you're lucky enough to be in close proximity to a large amount of teams, who will probably be more willing to travel to a tournament that offers a low travel cost. This will definitely work in your favor. I know for my program we would attend more tournaments if there were more in close proximity. We don't have an issue in time management or anything that keeps us from competing as often as other programs, rather it simply costs far too much for us to travel more than once in the fall, and more than one invitational in the winter.
And, another note, if you're worried about there being too many tournaments in the area, you can always try to contact a school nearby and offer to help them host the tournament or even just switch off each year, that way you can share the same pool of teams.
Best of luck Sam, I'm sure the more experienced tournament organizers/hosts will post or pm you soon to offer you more sound advice.
-Corey