I think some statistical perspective might be of some help. We can't dismiss your reman 16month/57K mile pack that has crapped out, and it would be helpful to know the average longevity of a reman pack before committing to spend $14K, but I'm not sure how many people can give you an educated estimate of how long and how far a Tesla reman battery pack should last. In my memory, I can only remember two instances on this forum where someone had two consecutive reman battery pack replaced within a 2 year period. We also don't know Tesla's reman process (and perhaps shortcomings), meanwhile 3rd party supporters are much quicker to explain their process.
Personally, I would try to get in touch with other Tesla Service Centers to get their opinions on whether a true reman pack is the only option. I would tow my Tesla up to 500 miles to get a chance of hitting the new "90 kWh" pack lottery. Otherwise I would go 3rd party and have the car either placed on a trailer or train to transport the car to TX or NC. Best of luck with this, I know it's something we all must dread.