You need to stay well clear of the elements.
To avoid errors due to insufficient insertion depth, the rule of thumb is insertion to ten diameters or more, though things get a little unclear when there's a depth of insulation to go through. The problem with going through the top is that you either have to bend the thermocouple or have it reduce the working height of your oven.
I tend to use 1/8" or 3mm Ungrounded Mineral Insulated thermocouples, inserted from the side just below the ceiling, joggled down so that they are just below the ceiling for a couple of inches or so. I normally go for type N, which was developed, along with Nicrobell sheath alloy specifically for Mineral Insulated thermocouples. They are Nickel-based and were developed to overcome some of the shortcomings of type K, particularly "drift" when used above about 1000 degC (1832 degF), without the high cost of Platinum-based thermocouples.
Drilling IFB is no problem with a normal twist drill, assuming you have one long enough. For deep holes in IFB, I drill a starter hole in the right direction, then use a tig/gas welding rod of the same diameter, cut with a pair of side-cutters (not flush-cut ones: you want a chisel-point on the rod) to continue the hole to the depth needed. I'm usually looking for a foot or more to pin IFBs together, leave the rod in and cut off the bits sticking out either end. The first time, I carefully ground a 3/32" Tig electrode into a D-bit, but soon found it wasn't necessary and that the welding rod worked fine. I think it works a bit like a gun drill (the hole doesn't wander) and the drilling dust from the IFB seems to get rammed into the pores in the sides of the hole (I wondered where it had gone when I was pecking with the D-bit and nothing was coming out). That said, IFBs vary and I'd want to do a test hole before making any committed attack on an expensive HT oven.
