Couple suggestions. Get some RTV High Temp Silicone to secure the fiberglass rope to the lid. The stuff they give you with the rope doesn't hold. Temp Gauge? IMO It doesn't matter where you mount it it will be off. Just put it where you want, measure the temp at the grate, figure the difference and roll with that. The temp will fluctuate anyway and as long as you're within ~20 degrees or so you're good. Heck Ovens are off that much, and this is nothing more than an oven, with smoke of course... Cheers!!!
If Homebrew & BBQ aren't the answer, then you're askin' the wrong questions... Cheers!!!