Hey texasman, you definitely want the 3/8", not the 5/8"... the 5/8 is going to be too thick and prevent the door from closing. Here's a vid I found way back when I was looking to buy my MF... you can fast forward to 6:40 to see the gasket kit Lowe's sells and the guy show's one way to install it later in the vid.
As for you question about a digital wireless...yes you can drill a hole in the side of the smoker to slip the probe(s) through. That's what I've done (see my post up above). I actually run at minimum 2 probes, one to monitor the chamber temp and one to monitor the product(s) being smoked, their internal temp(s). For the probe monitoring the chamber temp, you can cut a potato in half and stick the probe through it - with the point free and clear of the potato- and then set the potato on the same grate as the product you're smoking. This will give you the best reading as to what the actual temp is at meat/product level. I also run another probe for each piece of meat I'm smoking. I usually don't insert the probe into the meat until it's been in the hot smoker for at least an hour. This prevents the probe from pushing any bacteria on the meat surface into the core of the meat... that is a bad thing....
If you want to put a decent analog in the door - for a sanity check thermo - I've done the same thing. I installed a commercial Ashcroft but a lot of guys recommend the Tel-Tru. They make several different sizes...
Hope this helps.