The following doodle is going to look really rough, but I finally figured out a solution that had an even number of reflections and the merging prisms were doing the merge on either the horizontal or vertical axis.

Red arrows and surfaces mean it's an inverted image or takes in an inverted image. The 180 degree on the first blue arrow is what happened to the image after going through the collimating system. Most right angle prisms have been drawn as planes, but the first blue mirror is actually a merging prism.

In this case, the bottom green panel (green beam) reflects on a standard right angle prism before going through the merger prism. The top green panel (the one with the orange bar) (blue beam) reflects on the merger prism.

This merger prism is different from the one last log to keep the amount of custom parts to a minimum. It should now be the only bespoke component.

I'm planning to use a 15mm beamsplitter cube, so the actual merger prism would likely be something like:

It doesn't really matter how long that 5mm dimension is. It just has to be thick enough to not break. It could be increased to 7.5mm so that the dimensions are that of a 15mm cube with a trapezoid cut out. The real question is if I can use 15mm or if inaccuracies would mean it would be better to go with 18 or 20mm prisms.