Hi Denny!
Your rewire job is super simple, you lucked out. You basically just have to connect the white clips I circled in the image below.
The bottom clip has the smooth WHITE and smooth BLACK wire, that comes from your plug.
You disconnect that clip and take that end with the black and white wire and connect it with the compatible end in the top circle (will have matching end with red braided wires).
To confirm it is all good to go you just plug in your MES and the heating element should heat up. Try this on a regular outlet to eliminate any finnicky GFCI outlet behavior.
IMPORTANT!!!!! Do not leave this plugged in beyond confirming it is heating up. The rewired smoker is now dumb and will just heat up until it burns down if you leave it plugged in so don't walk away leaving it plugged in.
After you confirm it is heating up you now just hook the MES plug to the PID.
Drop the PID temp probe down the vent and hook under the bottom rack of the smoker.
Plug in the PID and enter the set temp and watch it go!
View attachment 692759
(For clarity, your lower circuit board is in that plastic black box where I circled the plug ends. A tiny flathead can remove those funky tri-slot screws they used to fasten the lid to that plastic box. You won't need to get in there since you lucked out with the clips meaning you don't need to do any wire cutting and splicing!!! )