I have a false bottom and a pump to recirculate. No problems.
For BIAB, I know some guys use something to get the bag off of the bottom. Trivet, colliander (so), or something like those.
That's the setup we have, false bottom about 3" high, with a recirc pump. This will be a new experience for me as we have always done the recirculating by hand in years past.
Similar to my set up. Some advice:
You need to throttle the pump with a ball valve on the output side. Pulling to hard can compact the grain bed, and you can collapse the false bottom. I know this to be true.
Keep the flame intensity medium low. To high and you can boil the liquid under the false bottom, and I have had the screen forced up, not good!
I have found that the habit of turning on the pump before lighting the flame is a good practice.
Stirring the mash helps equalize the temperature, and also makes the flow better, reducing the possibility of a collapse.
During the mashout rest at 168-170F, I throttle m a little more, let the grain bed settle nicely, and let the wort out of the pump clear.
So it is a balancing act that you will learn.
Hope this helps, have fun.