Actually rifles at late game are more useful than the sten because they do not get destroyed while trying to close the distance.
UKF has two nondoctrinal infantry options (not counting Airlanding Officer with limit 1). Giving Heavy Sappers LMG+Enfields puts them in the same fighting role as IS. That would be so boring, I can imagine better ways to set them apart. Just listing some of them:
1. Keep SMG and AT grenade (except with AT satchel charge option). Add something like demolition charges / heavy gammon bomb / AT or AI satchel charge/ heavy AT mine (M20/Riegel).
2. Keep SMG and AT Grenade, add smoke grenade or white Phosporous and two Thompsons.
3. Keep SMG and remove AT Grenade, give them some kind of more reliable PIAT (PIAT expert combat training).
4. Keep SMG and AT grenade and add a flamer (included this as an option inspite of dissent with you).
All four options would fit a heavy engineer thematically and would grant them their own distinct combat value.