Great - at least the problem is obvious.
My first reaction is to take it to a local alternator rebuilt shop and get a cost estimate to fix what you have --- or just take it apart and see whats wrong. Most likely bearings. Not much to these little alternators these days. Bearings are cheap from Grainger - local Auto Zone will rent you any special tools you might need - bearing pullers etc.
Repairing what you have lets you keep the basic OEM device, ensuring everything fits up as it should after it is fixed. Most local shops offer some kind of a warranty so there is some recourse if they get it wrong for some reason. Again it's not rocket science - just a magnet and a coil. I've had real good luck with letting local shops rebuild devices like this - Having a tech working one to one on it is far better than a factory assembly line - anywhere!!
I've purchased a few parts from both Hoye & DB - quality has not been an issue. Personally, given the small effort required to install it and non critical nature of the device, I'd give the $50 one a try - what have you got to lose? If you don't want to ever mess with it again - give Hoyle a try. I'd bet a weeks pay JD buys from the same vendor as Hoye but has them painted green! That green paint is extremely expensive - if you haven't noticed already!
Lastly, I'd go back to your JD dealer and ask for new belt -- at the very least - the only way to straighten these guys out, is to make them pay for stupidity. But you're right - if they had been smart, they would have sold you a new alternator at list price - plus a new belt and labor - consider yourself lucky!!
But it's not just JD, Beechcraft tried to charge me $2000 for a fuel tank cap!! (They make JD look like pikers) Fixed it (legally) for $50 - with a little help from my friends on the internet. ($5 gasket)
One more thought - There are several very good tractor savage yards around. Bet Western Kentucky Tractor Parts (https://wkytpstore.com/
) has a good, serviceable OEM alternator on the shelf. Good guys to work with - I rolled my 770 and broke it clean in half - they sold me all the castings and parts I needed to put it back together for very reasonable $$$. Major parts for these older tractors are getting harder to find. They are good folks to know!!
Take care & gud luck!!