How are you heating up the strike water (stove, propane burner, electric element in the kettle)?
I had good results using a thermometer with a remote sensor submerged in the MT to get the strike temperature as well as mash temperature. You could also install a thermometer in the side so that it's in a fixed location.
I'm not doing BIAB, but three vessel using PT100 sensors in all three that connect up to a single panel (controls everything). With the sensors in fixed locations, variations are small when they do happen.
You could also pick up a March, or Chugger, pump to recirculate the strike water as well as during the mash to get things more stable (temperature wise) for the duration. The eBIAB systems I've seen out there include a pump for such things (as well as running the wort through a chiller post boil).
Personally, I find the three vessel system to be easier to get my batches done than a BIAB setup. I did brew BIAB early on, but abandoned it due to it's limitations. Including needing to lift the bag out of the kettle at the end of the mash and limited ability (if any) to sparge. With my setup, I can do a mash then sparge either once, or twice, depending on batch size (if the batch has more sparge volume than will fit in a single run). Pumps play a rather important (basically critical) function in this setup. While they might not be critical for the BIAB brewers, they DO help a lot.