Before I answer your translation, I'd like to work with two others that I've seen that are a bit easier to understand.
The Sefaria translation is "halfway up the planks," not "in the midst of the planks." According to that translation, "pass through from end to end" would seem to be from one end of the Mishkan to the other, and thus you have no choice but to understand it as horizontal.
Artscroll's translation is "the middle bar inside the planks," as if there was the plank with a support inside and a coating outside, not unlike the way the Aron was built (25:10ff). This sounds more similar to your translation, and it seems to imply that there were beams inside the planks to help keep them sturdy. Thus, they were neither horizontal nor slanted but rather vertical.
If you take the JPS translation at face value to indicate one of the beams, without specifying which one, the question shouldn't be horizontal and diagonal, but rather vertical or diagonal. To this the various commentators to chapters 26 and 27 seem to indicate that they were vertical. (Logically, this makes sense as well. These beams were huge; if they were slanted even the tiniest bit, they would fall over with a big, loud, thud.) Though, this translation doesn't seem to explain what "pass[ing] end to end" means. Thus, I'm going to assume that JPS had in mind what Artscroll said.