At $10k you have to consider whether it is better to upgrade to a JL to be honest in my mind. Don't get me wrong, I bought my JK used a few years back because I did not want a JL. However, I would have loved to have the option to find a JK with an 8 speed. I do agree that it can be done for about $5-6k, maybe less.
I wonder, if we were to ping the folks who bought a new Wrangler in late-2018/early-2019, particularly those deciding between leftover JK's or new JL's, if the transmission/drivability was a major influence to their decision. I remember my first JLU rental, it was a 2019 white Sahara with the 2.0L. It felt considerably faster than the white 2018 JKU Willys I had as a rental just a few weeks prior. I couldn't tell about any gas mileage differences, since one was rented in rural Colorado (Durango) and the other in SoCal.
I don't fit well in the 2011+ JK interiors or JL interiors, so for me that was never really an option. Honestly I'd love a 392 Rubicon but I could never write a check for that much $$$ and have a vehicle I could barely drive for more than 2 hours at a time (they both kill my back/shoulders, as I'm forced to "lean" away from the door to get comfortable).
Given the cost of a JL, plus their quirks and known issues, it would certainly come down to preference, willingness to spend more $$, and consideration of money already spent. For example, if you've got a nicely built JK and are looking to extract some better drivability, $5000 is fairly inexpensive (though realistically it's probably half that for most DIY'ers). Couple that with the nightmare of selling your JK, recouping as much of a % as possible on parts you've added, then buying a JL and replacing those parts you had on the JK to get it to the same level.
At this point, I think for the money (being quoted just under $2500 for the 4:88 swap) I think I will see how that perks up the old girl.
To be fair, no engine or transmission combo will completely make up for improperly geared axles

The 5.13's we put in my daughter's Islander made a massive improvement and was money well spent...