I am trying to get the shaft to run at 3600 rpm. I don't know if it will slow down much under a load. Would the AC be too unstable or would it be better to use a DC battery bank with an invertor?
The #1 problem you will have is transmission. You have power at location X and you need it at location Y. And heating is a big load: you only get 3.41 BTU/hr per watt.
I hear you arm-waving it as "only 100 feet" but that's exactly the mistake everyone makes! Seen it over and over*. Let's fast-forward through the rest of that mistake chain: the person skips doing a proper voltage drop calculation because they kinda know the answer (in copper) won't be pretty, so instead they buy the copper they're willing to pay for. It's not nearly enoug, not even close; voltage drop calculates out at like 60% which makes the system not work at all.
They blew it because they were brain-locked on copper as the only viable conductor. Actually, the US AC power system and its supply chain is designed around aluminum as the principal heavy feeder. Dirt cheap commodity aluminum wire is the best answer - for low voltage DC you typically use duplex URD, or 4-wire MH feeder in 2 parallels. Same with SER indoors. With this very affordable wire on tap, now the Load Calculation isn't so frightening, and you can size your wires properly. Doing that Voltage Drop Calculation is a good teaching moment, too, because now you know for sure. A lot of people never figure it out.
Splicing from Cu to AL wire is straightforward using lug connectors. For #4 or smaller, just cut up accessory ground bars. #2 or larger, use bare lug connectors (no need for the costly insulated Polaris connectors; you can hand-insulate 24V). Note that all these lug connecters are made of aluminum, because when aluminum is the lug, thermal expansion differences Cu vs Al work favorably. Thus Al lugs are the universal donor. Torque screws to spec.
* Pure Living for Life did the same flub with their early solar panels, using #10Cu, back when 2-2-2-4 was a buck a foot. They "got back on the horse" and tried solar again; though in the end they relented and brought in utility power. If it was easy, everyone would be off-grid :)