How does distance between parallel batteries affect voltage drop/required wire thickness?
Yes, basically you have it right, more distance means greater voltage drop.

So, best thing to do is locate the batteries safely with proper venting, then consider your cable run.

To limit the voltage drop, which is due to the resistance of the cable ie proportional to length and inversely proportional to diameter, all you need to do is put in a nice thick cable which will compensate for the length.

So, if the maximum current from the batteries is 20A, then the cable is relatively cheap.
If the current will be about 100A, then you are looking at the size of cable used for car battery to starter motor - which as it has more copper is more expensive.

Good cables and decent connections are cheaper than a fire...