There was a somewhat brief period back in the 1980s? 90s? when some photo processors offered 8x12 prints from 35mm. I often wondered why that wasn't more common, but finding suitable frames was likely part of the reason. There are some varieties of "sectional" frames where the sections are sold separately in pairs of various lengths. That allows creating a 10 x 14 frame or 8 x 22 frame, or whatever floats your boat. The only obstacle with that is you are likely on your own for mats and glazing. Mats can be cut with a Dexter hand cutter and a straight edge, though I won't say it's not tedious. Acrylic glazing can be cut using a scoring tool, and glass is scary, but not actually that difficult once you've done it a few times. I suspect most "glass" shops would do that for less than an arm and a leg. There are online suppliers of frames that will do at least some selection of custom frame, glazing, and mat sizes. Generally that is more expensive, certainly more than off the shelf stuff at MalWart or the like, but some of the online sources are surprisingly reasonable.
Another approach is to use a frame somewhat larger than you might normally choose which helps make the difference in aspect ratio between print and frame a bit less obvious. For most of my recent history I've been cutting my own mats -- occasionally even made a frame or two -- for a few oddball projects. I frame my square prints, about 10 inches or so, optically centered in a 16x20 frame; get an occasional pat on the back for presentation.
Another approach, which might beg for a four-blade enlarging easel, is to print the image in the center of a larger piece of paper, one large enough to install it in a window mat with a larger opening and let the wider borders of the print fill in the area around the image. What to do depends a bit on your vision for the final presentation (and maybe your bank balance!)