Your drawing and description looks good.
I'm cheap, so I use one pump and my hoses have cam-locks for moving to each step.
Keep your pumps high so there is less hose volume, and the pumps and hoses can be drained and collected.
There is a way to control the flame with a PID, but I'm not familiar with it, so I can't really comment on that question. I do know that it's pretty expensive to add the pilot and control valves, plus the PID. I chose to spend less than $100 on an electric RIMS tube. Electricity is cheaper than gas too, and you won't run out of electricity.
For chilling/whirl pooling:
You're using an immersion chiller (IC) I assume?
Use the pump to recirculate while you chill. It will stir the wort and help cool it.
Then, after the wort has chilled, remove the IC and direct the pump flow to create the whirlpool.
Once the whirlpool is established, turn off the pump and drain the lines without disturbing the whirlpool.
Wait a good amount of time (~20 minutes) before carefully removing the clear wort leaving the "cone" of trub behind.