One suggestion I threw around a while ago was giving Thompsons to RE as it would make them a cheap flanking unit that could force off support weapon teams and even threaten weaken enemies. On a side note giving a Thompson rack would have little benefit due to the fact you can get BAR(s) that perform better at all ranges besides being somewhat less effective at close range.
Thompsons would be cheap, perform better on the move than BARs, and would make Volley Fire pretty good due to its fire rate. No tech Thompson racks would also go great with usage of smoke.