I think putting it on PA letterhead is appropriate. Our PTA has it's own letterhead and we use it for all of our events, etc. I do agree with your principal on this one too - if it is asking something for the children, or something benefitting the children, then it is okay to use the school letterhead. Good luck!
In the past, our PTO has asked local business for donations that we can then use as raffle gift items for our Teacher Appreciation Week. The teachers get some really nice things - pedicures, gift baskets, etc.
Most places that we contact ask for the request to be made on school letterhead. This year, our principal does not want to approve the letter on school letter. He feels it is in poor taste for something on district letterhead to be asking for something to be given to the teachers.
HE is okay with it when we are requesting things for the students or an event, but not for the teachers.