Kool, here are a couple of thoughts that might be helpful:
Disassemble the Jacob's taper and have a look inside.
If things aren't pristine on either tapered half, that's your problem.
If the taper is fine or only lightly galled you need to properly seat it with a lead mallet. Open the chuck until the jaws have receded into the body. Put the R-8 end down on the hard floor or an anvil, with a piece of Aluminum, Brass, etc between the R-8 and the floor/anvil.
Give the chuck body a couple of solid hits with a lead mallet. Don't be shy, let it know who's boss. At the same time, don't beat the hell out of it.
The above MUST be done on a hard surface. A wooden workbench will absorb the majority of the impact.
Unless the chuck has the smallest Jacob's taper, it should be capable of driving your 2" hole saw if you're careful. While side-loading is an issue due to the reactionary forces acting on the taper, I've never had a Jacob's taper walk out with a hole saw of that size. Not saying it can't happen though!
Speed should be about 80-120 FPM (225 RPM or so) with sulphurized cutting oil. Too slow and the teeth well tend to grab. Too fast and you wear them to nubs.
If that doesn't fix your problem, I'd look for an R-8 arbor with a 5/8" threaded mount. Then, find a 5/8" threaded-back chuck. That WILL solve the problem!
