I understand that when Reamping it is necessarry to apply a reamp box to the signal coming out of the interface, in order to get the signal back to being high impedance as it is when it comes out of a guitar.

I am looking for a patchbay, to be able to make all of my connections in one place, including guitar>patchbay>pedals. I see that mixers and alot of studio gear seem to assume a low impedance line level signal will be present.

Does plugging an unbalanced hi-z guitar signal directly into a patchbay that uses balanced ins and outs change the signal from hi to low impedance and require a reamp box? Would connecting my guitar to a distortion pedal via such a patchbay mess up my tone as compared to plugging into the pedal directly?
Use di box and re-amp box always if possible. The high impedance signal does get worse over distance(or longer cables). Using a low impedance for long runs and switching right next to the source with di/re-amp will preserve your tone.

I would go to a di with a 2m cable. Run balance low impedance to patch bay up until the amp
Place a re-amp on the amp an use a 0.3m wire to connect to amp.
I've used patchbays in the past and honestly the more gizmos you put in between the more it will drop in sound. If you're using unbalanced cables on both ends, the patchbay would just work as a passthrough box essentially, but there are different ways use and thus to wire a patch bay, tutorials for which could be found online. A patchbay won't solve your signal conversion needs, it could simplify them in terms that it will put your connections in front.
A DI box in reverse works almost as good as a reamp box, maybe it is a little noisier but that's what I've used in the past (Radial passive DI) and the difference is not that great (I have Radial PRO RMP now).