Good question.
It can be frustrating to find the right size/ratio/matte/frame combinations that work.
The larger the print is relative to the frame the more important it is for the matte thickness to be equal on all sides, otherwise it looks strange. For the 2:3 ratio I often use a 16x24" frame so I will print to 16x24" paper with a 1.5" boarder on all sides so the actual image is 13x21". Similar to your example above only smaller and in 2:3 ratio. If the same 13x21" image goes into an 18x24" frame (which seems to be much more popular and not native to the 2:3 ratio of a DSLR sensors) the matte/image looks unbalanced within the frame. If the picture is quite a bit smaller relative to the frame then keeping the same thickness of matte on all sides is not as important. For example, an 11x14" matte looks good in a 16x20" frame.
Ultimately I won't crop an image for the sake of the frame and I'll make the frame/matte decisions based on the size of the print I want to make. My experience is only in pre-made frames, and I'm no expert, clearly. It would be much easier to just have a custom frames made to fit your needs, albeit much more expensive.