Paperwhite Gen 6 should be the 2013 model, I'm not sure where you are located for shipping, but I have been happy with this site where you can buy a replacement logic board.
https://www.powerbookmedic.com/Amazo...3-p-46083.html
So if the screen and everything else is good, you could just replace the logic board ( if you really want to buy the MMC chip and replace that, go for it, but this is a lot easier :-) )
The only one they have in stock is wifi-only with Special Offers though.