I have been a BIABer and a recirculator.
You don't need to worry about scorching if you use an ultra low watt density element. I have had the bag sitting on the element with no problems.
You can do this without recirculating, just stir a few times and be done with it. You have to keep a very low level of circulation or you will have a compacted grain bed. With that low of a circulation rate, the PID tends to have a hard time maintaining the correct temps.
I have recently just set my pid to 5-10% in manual mode, stir a few times during the mash and had better results. So I am still doing BIAB but skipping the recirculation with a pump.