I just wanted to report back, especially for anyone stumbling onto this thread with a similar question.
I decided to leave the air mattress at home and instead use a cot I own that I have also always found adequate (this one + this liner + a blanket and pillow). It measures 73" long, 27" wide and 15 to 20" high (head is higher than feet). As you can see from the photo below, there's ample space around it.
Could that area fit a twin air mattress? I think it might be possible. Unfortunately I forgot to bring a ruler or measuring tape to check definitely, but this cot option definitely works for anyone that might have similar requirements.
The only thing worth noting is I used up an entire luggage to store the mattress pad, blanket and pillow, so if you need your bags, this might not be the best option for you.
I also decided to check in the cot itself to make things easier for me (it's big!), but I think they might've let me carry it on too since I had it over my shoulder.
Hope that helps someone :)