When I turn my key back to ACC, my voltmeter reads a strong 12V. But when I turn my key to run, it reads about 10V. Either way I try and start the car, by key switch or jumping the starter relay it will crank over slowly, even with a full charge. Any idea where the most probable place to look is? I was thinking the switch may be bad, but it cranks the same jumping the relay?

bad batt(cell)/bad starter/dirty large cables. I'd start by cleaning every terminal starting at the batt positive post then the same on the grn incl starter to block, the complete circuit. Starters are strange electrical motors, the slower they turn the more current they draw & reduced current from a bad batt or cables will slow it which draws even more current which slows it more & this happens in split seconds. I'd clean em up & c what happens

Yeah, I'd start by cleaning them up too. You'd be surprised at how much tarnish/corrosion you can find. My wire to my starter looked pretty good after cleaning the connection at the battery, but I was still having similar symptoms to yours. So I cut the sheath away from the entire length of the wire and its was BAD how much tarnish was there. I cleaned it, put some new insulation back over the wire, and my problems were over. I could have bought a new one, but I fixed it for free and learned a valuable lesson at the same time.

Also, if you have the stock style starter, you may think about a mini starter. These things are amazing, as long as you dont care about original appearance.

The starter draws 120 amps..
If the battery, terminals or cables have poor, corroded connections the voltage will sag until enough current is available to spin the starter..

A starter can get weaker due to internal issues but in most instances the problems are related to battery and/or cables..

Just my $0.02...

..in 'start' the ballast is by-passed to apply a full 12 v to your electrical system because the voltage will drop to 9 or 10 volts due to the heavy starter current.
..once started the switch will be in 'run' and flow will be through the ballast which will also drop the voltage to about 9 or 10 v which your system is designed to operate at.
..your values seem normal
..maybe a bad starter,poor connection or an engine problem.