Note that the Elite Armour doctrine suffers from being a bad doctrine carried by an OP Sturmtiger.
HEAT rounds are OK, but why pick them when Command Panther gives you a generalist tank PLUS aura PLUS a better-scaling buff?
Same for vehicle maphax; Command Panther doctrine gives you a better version of it that also improves your indirect fire accuracy (since it clears FOW) and allows your allies to fire indirect fire at will.
IMO the solution for the doctrine is fixing Crew repairs and Tank Commander, make both abilities solid for 1v1, and then smack down on the Sturmtiger so that it's less OP, and if possible also less situational.
Why not to make it like a mobile howi?
Unit which cant shoot on move, and it must be set up to fire its round. Imagine it like marder\PIV from PE in vCoH or KV-2. Leave same range or maybe even increase it a bit.
Set up time into "firing mode" should take about 4-5 seconds and same amount of time to move out of firing mode. Reload can be started only if firing mode is active.
In this case, you would have to make good preservation and pick good location to be able to use ST effectively. You would remove ability to hit-and-run but still would keep unit at the same power and usefullness.
While the idea is good, what I'm afraid that will happen is it will make Sturmtiger even more situational than before.
If you have Recon, then you are basically hardcountering the unit, as you will never walk into its arc of fire. If you don't, and the map happens to have buildings close to an area of great importance, then you can do absolutely nothing.
If Sturmtiger can't fire through shotblockers, then yes. All factions have counterplay to the Sturmtiger.
Alternatively, if the Sturmtiger can no longer oneshot mediums, then you can always have the option of yoloing through a chokepoint; you will still take losses, but you have better odds of getting the Sturmtiger.