No need to experiment, the numbers are there provided by Cruzz. Rifleman with 1 BAR DPS outperforms STG 44 Volks DPS at every range. Low range DPS is over 150% more. Only mid range is close, but still about 120% afaik.
Not sure how you arrived at this conclusion, does this include the other members dps with rifles?
Here are the numbers from the Cruzzie files for the upgrades:
USF Riflemen BAR (60 muni each)
DPS: 13.2 / 6.5 / 4
dists: 5 / 14 / 35
Volks gren mp44, single (30 muni each)
DPS: 7.52 / 4.5 / 2.0
dists: 7 / 23 / 35
Note that the BAR has a very short mid range, making it only really effective at closer ranges.
The double stg44 is clearly better at medium and close range, while having a better effective range than the BAR. The stg44 upgrade is the more cost effective upgrade than the BAR but USF has the option to double equip.
Edit: forgot to mention rifles not included.