I have the same machine and I got it too hot once and the magnets in the flywheel shifted (must be glued in). Same as yours, it ran poorly and would stop or sputter occasionally. I had a mechanic replace the flywheel and it has run perfect ever since.
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It definitely helps if you can work with a bigger dealer with multiple stores to increase the chance of having something in stock. With the loader and all fees minus rebates, it was just over $33K total. That was with the 12/12 transmission.
I purchased a 5065E last year and without the loader, MSRP was $34,980 and the dealer quote was $28,500. I don't remember the breakout of Deere discount vs. dealer discounts. I have found Mutton Implement's (Deere) website to be a good resource for what to expect a competitive dealer to charge.