Your other option could be to stay at Glenelg. The Stamford Grand or the Oaks would have reasonable rooms with a cheaper price. Although I have never stayed in either (I live in Adelaide), it would make sense to be at Glenelg which would be a 5 minute drive to the airport.
Join Australian Frequent Flyer (AFF) for free and unlock insider tips, exclusive deals, and global meetups with 65,000+ frequent flyers.AFF members can also access our Frequent Flyer Training courses, and upgrade to Fast-track your way to expert traveller status and unlock even more exclusive discounts!