I just went through this!
If you call during the day (I think 8-5 EST) and call the MAIN number. Ask for the ticketing office (not ticket reservations). They will be able to take as many gift cards as needed. We had $900 worth and it wasn't a problem. However, the first DVM CSM I talked to said the same thing yours did..only 2 forms of payment per ticket. I'm pretty sure the difference is talking to the ticketing office rather than the vacation specialists. I'm thinking that the office must be on Disney property and the vacation specialists at a call center somewhere. I can't remember what the number is, but I know you have to press "5" after you call it. Just keep asking until you get the right person.