I presume that the part of the stud that is stripped is the upper threads, right? If so, there are a number of ways to get the stud out, including vice grips as suggested, a stud puller (I’ve had the best luck with the eccentric type, not the jaw type, although others may have a different viewpoint), or welding a nut down low to the stud. The advantage to the latter is that you’ll put the stud through an expansion-contraction cycle, which may help break it loose. In any of these you can try without removing the head, but if unsuccessful off the head must come.
If you are saying that the block is stripped, different matter. You would need to install some sort of insert like a Time Sert or Helicoil. Use a jig or drill the hole with the head installed, without it’s real easy to get your drill canted and make it very difficult to get the head on/off a tilted stud.
As far as reusing the gasket - no reason to not try, especially if you get the stud out without pulling the head. If you do pull the head, the cost of a new gasket (what, $40-$50 or so?) compared against the hassle of pulling the head again if it doesn’t seal would seem to me to favor replacing it with new regardless.
You say you are using a Best gasket. I’ve never removed a Best graphite gasket without destroying it.
In my experience old head bolts are so heat hardened that they are very difficult to drill out with conventional drill bits.