What a fascinating application! This is great sort of stuff for poking out the corners of what a technology is capable of. I'm going to be thinking about that for days, I feel sure. Here are a few thoughts off the top of my head.
First, don't get married to Li-ion batteries. I'd very seriously look at NiMH batteries, which can charge and discharge extremely fast. Your application isn't going to need much capacity -- it's over in seconds, after all -- but you'll need a very high discharge rate. Yes, supercaps can do that...but they're pretty expensive, and their voltage sags as you discharge them. I don't think you want your saw getting weaker during the run. NiMH batteries can give you very high discharge rate even with a fairly small battery pack. For instance, my RAV4 hybrid uses NiMH batteries and is spec'ed to have a ONE KILOMETER electric-only range, so you can see the battery is very small (they don't give the actual capacity). But the electric portion of the drivetrain is rated at well over 100 horsepower because of how fast the battery pack can discharge, given its small size. It also charges very fast when the ICE is running.
If you do want to go with lithium, look at LiFePO (Lithium Iron Phosphate) batteries. They don't have as much energy density as some of the other Li-ion formulations, but again, you don't need much capacity. LiFePO is capable of far higher discharge rates than most other Li-ion formulations, as well, which is what you really want.
As far as the actual capacity you'd need, for reference, if you wanted to put out 100 hp, that's about 75 kilowatts. If you need to do it for 20 seconds, say (just to be sure), that's only 0.416 kW-hr. The energy density of LiFePO is about 130 Wh/kg, so your LiFePO battery pack could weigh as little as 3.2 kG, or seven pounds. NiMH stands about half that, so you might have a 14-pound battery. Just a week ago, a team of researchers announced they'd achieved a record energy density for supercaps, at 88 wH/liter. I don't know how heavy a liter of supercap is, but it sounds like it's at best competitive with the LiFePO -- and it's not available OTC yet, it's just in the laboratory. I'm sure it's REALLY expensive, too.
As far as motors go, you're probably in the right place. Some of these electric motorcycle motors are very much in the ballpark of where you want to be in terms of power, and they're not all that heavy. I'm guessing you could find something in the 35-40 pound range with somewhere in the 100 horsepower output, lighter than your Rotax with more power and torque.
And I'm thinking you're right, all that torque might be a bit of a beast to handle, and hard on stuff too. Fortunately, however, everything's controlled electronically, so it seems like you'd be able to keep rpm from ramping up too fast, or exceeding a safe maximum, which would solve your startup and runaway problems (which you might experience if a chain breaks).
It sounds like a lot of fun, and honestly, a good application to take advantage of the very high output per pound of a good electric motor. I hope you'll keep in touch with us and let us know how it goes.