The limit to number of payment methods only applies to the purchase of DVC APs when purchasing via MS. By phone, each gift card is counted as a method of payment.
You can use as many Gift Cards as you need to pay for the Dining Plan, but you must call to do so.
I purchased the DDP for 8 people using 41 $50 Disney Gift Cards over the phone with no problem (except that it took a long time to read all the numbers!).
Great thread to have out there Lexi. So much erroneous information out there about this matter.
I was convinced - because I had numerous low amount Disney cards - that I couldn't pay for my dining plan. Because there were threads thinking/stating that it was for dining plans as well.
I'm glad I phoned and was pleasantly surprised that the rule was not for the dining plan.