I see. I played around a bit and can confirm that deleting the coplanar faces and making the 4 solids planar before unioning them fixes the problem. I am surprised this turned out to be the problem. I thought that the edges overlapping with the cutter is what was the problem, the fact that scaling by 1.001 worked for me only served to cement that hypothesis. I thought I was making a trivial question here, but the answer was wholly unexpected for me.

Considering the edges were so far away from the cutter, why were they a problem?

I see that if I separate the solid, the cut works, but it is a bit wonky on the vertical parts and I am not sure how to join it back in that situation.

Also thanks for the note that the points in the cutting object were overlapping, it slipped my mind to think about that. I had no idea that show points would indicate the duplicates.