Well, this is one of those areas in life where you get what you pay for.
Cheap frames from the discount stores, Michael's, et al. are just that... cheap, generally poorly made and not anywhere close to archival.
Personally, if I have gone to the trouble to make the very best print I can something that is "frame worthy ", I am not going to compromise the final product with a discount store frame. That goes for prints on my own walls and doubly for prints that leave my house as gifts.
I try to keep to standard size frames, but when I need an odd size I almost always use metal frames where you can buy pairs of frame pieces in many sizes. Buy two pairs in the sizes you need. They go together easily and cleanly with a screwdriver.
I often use framedestination.com for these, but many art supply stores carry Nielsen Bainbridge frame sections that are a bit more expensive but can be had without needing to wait for delivery.