Doctrinely speaking, HTs were seen to have two purposes:
1) Keeping up w/armor
and
2) Tactical ferrying of troops. Look at any WW2 manual and you will see stressed the fact that they need massive overwatch and careful movement.
The Germans normally deployed from trucks and HTs 500-1000m short of the objective.
In the American Army we still use the term. I teach very basic tactics and I can assure you it is still alive and well. I believe the WW2 term is "covering fire". Based on my Uncle Arts WW2 version of the FM 7-8, that is.
I was a Pig gunner ( and my own Assistant Gunner, which meant I got to carry my tripod, spare barrel, TE device, gloves and tools. A simply outstanding system. Easy to use, easy to maintain. A real bitch to hump.
Once you get behind them, use engineers or bazookas to blow out the back. Regular infantry can also work.
But look out for his security element protecting the pillbox.
Smoke! Use your smoke to mask youyr movement!
Suppress the pillbox with other units.
Smoke your assault teams path.
And then go in with hiopefully some engineers with demo.