The idea that you will get better prints at exactly 300dpi — where one dot is also one pixel — is a misconception. There may have been a limited time and certain circumstances where it was true, but that's not the case now.

There is no harm in having more pixels. You should be able to find 12×9" prints and frames relatively easily, and print at around 350ppi with no concern. (Or you can crop to one of other historic aspect ratios.)

If your concern is that 4288:2848 is not exactly 2:3, I urge you to relax on that a little bit as well. There's "a little picky" and then there's "not reasonable given the real world". The difference is 52 extra pixels in the long dimension — or 1%. Not only is this not noticeable, it is likely well within the tolerances of a frame that's nominally 12×8" (or similar). More so, you'll have a hard time making prints with the border that precise — you certainly won't get it with a printer that has a borderless option. You'll need to print larger and carefully trim yourself.