Just let it fluctuate. If you don't you will be "chasing the temp" which will make the cook miserable and is very labor intensive.
The egg responds slow at low temps so if you try to open it when temp drops you will open too m…
Almost sounds like my brick chicken only I marinate for a couple of hours and then indirect cook it with a couple of bricks, done in about 4o minutes. I'll have to try the spatchcock and compare. that's for the tip.