First of all the differential from an auto works like this:

The driveline turns 1 revolution, the ring gear is driven from the pinion at a specific ratio (ie 4:11. 3:25 etc.). The ring gear interacts with the spiders and drives the axles. The axles turn in proportion to the pinion, like 11 revolutions for 4 turns of the driveline in a 4:11 rearend. MOST differentials do need the "off" axle locked to do what you want. So to gear up the speed of the alternator the axle side is where it needs to go, and the prop or input to the driveline side. Be aware that without some type of pumping the lubrication will not be right, but that can be overcome easily. NASCAR rearends have pumping systems for cooling the grease driven off the driveline.

I would not use this setup for anything other than a BIG Savonious type mill. Or maybe a BIG hydro system.

Newer 4WD vehicles, and cars do no have a full axel across the back.

The back kinda looks like the front, as far as drive train goes.
Two half shafts, one to each wheal.
There is a  gear box in the middle that the two half shafts plug in to.
And a drive shaft that goes to the gear box from the front.

Rear gear box is about a foot or so wide, and a foot or so tall.
And some times up to two feet long.
It usually has two taper bearing that support the rear differential.

If you feed a rod through the unit with the blade ran to that,
And have the differential function disabled, and you will have a nice
1 to 4 (or close) gear box.

if you lock one axle and force the differential to power the pinion thru the spider gears you will double the ratio and get anywhere from 6:1 to around 8:1

as for lubrication, as long as the pinion is parallel to the ground such as it was in the car, the ring gear will pickup the lube and circulate it as designed. you also could go to a lighter gear lube to cut losses, but be sure to have a GL-5 rated lube in any event as the ring and pinion gears mesh in a wiping motion, thus the need for the friction modifier that GL-5 affords.

as for friction losses you are likely going to lose around 10% or slighly more, if you have a sufficiently large rotor, maybe this is an acceptable amount of loss.

you might also consider either the cog belt (timing belt) or a serpentine multigroove belt drive, either of which is more efficient and lighter, and require no lube. If you incorporate a tensioner from a car, you should get pretty good life out of it with little slippage loss on serpentine drives, and no slippage of course on cog belts.

as for power capability, the serpentine, microgroove belt in the 8 rib variety will handle approx 20 hp or so, and live to tell about it.

also if you use the microgroove belt, they can be driven from the back side, eliminating the need for a large grooved drive pulley, you could use a 20 inch in diameter drive hub with a smooth outer diameter, run the belt over it backwards to contact the hub, then take it over the driven pulley on your alternator, and on the opposite side run the idler to provide the tension and auto takeup of the belt.

just remember to try and get at least 40% of the pulley in contact with the belt, either driven or drive, 50% is even better.

on the plus side is if you run the belt as i have described, it can be changed out without removeing any shafts or the alternator, all you would have to do is pry the idler back and swap the belt.

microgroove belts are common on all cars these days, and started out as drive belts on detroit diesels on GMC trucks back in the late 60's. It is not uncommon to see them run well over 100,000 miles on a truck.

personally i think that this is a better option for you.

is this the one you are speaking about?

http://www.otherpower.com/images/scimages/60/e_alt.JPG

Looks really interesting.
Which kind of alternator are you using?

In any case I think that a car differential
is one viable alternative for big machines.

You can take the power
all the way down on the
the earth by using axles if you are
using a car differential.
And if you'll use
a second hand whole rear axle
of a small truck you'll
get ready made bearings
of the wheel for the
wind rotor cheaply.