Would it be possible to rearrange the recipes that have two pipes with the same fluid, to have those two pipes be placed across from each other? This would allow a row of machines of the same recipe without funny pipe placment.

Unfortunately, no. I wanted to do that, too, but as far as I can tell the factorio prototypes do not allow this option. This is because each fluid connection in that type of building has to be define as either input or output and can't be changed at runtime. I tried applying the "input-output" fluid connection type, but this type is only available, as far as I can tell, on the boiler prototype. I used to use a trick where I could put input and output fluid connections on top of eachother, but that trick was eliminated from the engine in late version 17. Now it errors when I try to do that. Probably for the best, since this wasn't a supported mechanism.

These are more reasons I considered when designing Adamo Chemical, which uses some buildings other mod authors have graciously allowed me to turn into alternate chemical plants, and those have various options for piping chemicals through and arranging things in different ways. Due to factorio prototype limitations, those solutions aren't perfect either, but they do offer some flexibility once you get used to the limitations.

FWIW I tried to make this work as well. As far as I can tell there are 3 valid configurations here:
1) Let factorio automatically set up output points, as done now. Works, but the pipe placement is messy.
2) Specify 1 output point for each chemical in the recipes. This lets you get, for example, HEU hex directly across from the input, with DU on one of the sides.
3) Similar to 2, but you can specify 2 output points for DU, and they can be across from each other. Unfortunately I cannot find a way to do this while also having the fluidboxes connected like the automatic setup, so you have to divide the output in the recipe, and you will be forced to drain both outputs in production. Obviously, this is really ugly.

Of those options, I think I prefer #2 myself but not by a large margin. If there are reasons to keep it as is, then by all means do so.

I've tried organizing the recipes every which way, believe me... because I was using virtually every feature in the fluid system in version 17, I was able to find weird edge cases under a lot of conditions people might not think about. I ultimately settled on what I have now as the best balance under what I considered to be the best organization of the buildings -- I believe I put that in a picture on this page. Take a look at the last picture on this mod's page. I believe that picture shows the symmetry I was going for when choosing the default outputs that I have here. But truth is I use the Fluid Permutations mod like a mofo. I need to do a major overhaul of this mod to bring it up to the modern standards my other mods have. :P So yeah, I dunno, I tried to find a balance, but I'll put together another nuclear setup on my version 18 testing ground map and play around with any suggestions.

Can you have multiple input fluid boxes then? that shouldn't cause an issue with one being empty, right?

If I understand you correctly, I don't think so. The problem is that I can't designate a fluid box as both input or output; it has to be one or the other. Since the building has to be able to handle 3 outputs in the more-complicated case, that means it can only have one designated input. You can see how I solved this with the Still. I hacked in a second input using an underground connection with a tiny, nearly invisible, offset.