Find a good automotive-electric repair shop. The kind that specializes in alternators and starters. make sure the firm "marinizes" their work and you are set. I have a few of these shops down here in Florida.
     Heck, if you cant find a shop where you live, the shipping costs would be worth it to avoid the $715 bite!
     I had my alternator rebuilt and upgraded for a measley $75.00. It went from having an alternator that wasn't putting out squat to an robust 70 amps. Compare that to a new unit that went from $395-800.

     I was chatting with the local BMW (boat maintenance worker) and he had a comment about my little Westys' poor cold weather starting capability.  He suggested having a battery company make me a starter cable out of  #1 gauge cable.  He remarked that most battery to starter cables were made for perfect conditions.   Factors like cold weather and the eventual cable corrosion that sets in can limit the available amperage to the starter to the point that it cannot spin fast enough to start a diesel.
     I would imagine that the reduced power would also put a much larger strain on the starter and negatively effect starter life.  He had stated that by doing this on several Catalina models he had fixed problems that  starter rebuilds, larger battery installations, etc. had failed to fix.

     Sounds like a bad throw out bearing (I think that's what they call it.)  I have never taken an A4 starter apart but technically it must be the same as an automobile starter and there are replacement parts in them.  Its rare that a starter has to be rewound. If you do not feel comfortable taking it apart yourself, find a local starter repair shop and have them test it and tell you what's wrong before spending megabucks to replace it.
     There are also a lot used A4 parts around the boating community. If the your starter must be replaced, check around the local boat yards or talk to other A4 owners in the area or here on the listing for some leads.  A used starter was probably running just fine until someone decided to scrap the engine.

     You've gotten some good advice on how to deal with the starter and beef up the battery cables. However, since you say the starter does work but only at one position, this suggests that the problem is the relationship between the starter gear and the flywheel gear, rather than the starter itself.
     You did say the teeth on both look good, but you may want to double check.  Be sure you are looking at the Flywheel gear teeth from the side the starter engages them - not the easy-to-see side, front of the engine.
     Typically what happens in IC engines in general is that they stop with the gears in only certain positions, due to compression and piston location.  This means that each time the engine was started over the past fourty years, the gears experienced wear in only those few positions. The gears may now be so worn that you must persuade the engine to some other rotational angle (between the wear spots) before there's enough bite between the gears to get it spinning. Once it starts to spin the total load on the gear teeth is less, so even tho' they're worn and noisy the engine will usually spin enough to start. Usually it is the ring gear on the flywheel that wears the most, not the starter gear.
     If worn teeth are the problem, replacement of the gear(s) is in order. My Atomic 4 Parts Manual does not list a flywheel ring gear as a separate part, so it may be that the gear teeth are machined directly on the flywheel (but I doubt it, this is not usual for other engines - also, it refers to the "flywheel assembly"). This may be academic, since you're more likely to fine a used flywheel than a new ring gear anyway. If it turns out that this is what's wrong, and you do come up with a ring gear to fit on
your flywheel, sing out and I'll describe the procedure for replacing it, using only equipment you already have in your own kitchen.

     The fly wheel is one big solid piece of iron, easy to remove, or just take it off and rotate it and reinstall it so that the point that it seems to want to stop in will be a new place on the wheel. Good luck.