I remember you stated you could not run the interface beyond 9600bps as well without corruption issues. Both the range issue and the UART speed issue could be related to an issue with noise in your circuitry. Electronic noise can be caused by a variety of things...
Switching power supply (buck/boost converter).
Long traces.
Poor trace contact.
High ground resistance.
High wire resistance.
Switching devices (processors, crystals, etc).
Etc.
I would try to find a way to reduce your trace length (or fly wires) much shorter. I would also try to bundle them together, particularly close to the ground wire to shrink the size of your ground loop.
If you can I'd recommend mounting the modules to a PCB, it may be the only way. You could use a service such as
OSH Park. The lead times are long but the costs are low.