The hint told me "peppers" without any hint of case (but I knew it CAN be nominative plural form). I am saying the translation ("I do not like peppers") is very misleading for those Polish learners who should focus on singular and plural cases, because in this case, it should be genetive and not nominative. Saying "peppers" alone is fine, but "I do not like peppers" is completely misleading I believe. I would recommend saying something like "I do not like the pepper."
Interesting… Must be a regional thing, I accent "papryka" on second to last, initial stress sounds a bit odd to me, tbh.
From the list you linked(I didn't check all, it's pretty long), I also use second to last on: kronika, muzyka, ceramika, polityka, praktyka, erotyka, fabryka, fantastyka, robotyka, informatyka, turystyka and klinika.
But the rest of the list(at least the words I checked) I also pronounce with accent on third-to-last, so I guess I have some sub-standard pronunciation. ;-)
Check out this article on why you should not worry too much about your accent when speaking Polish: http://blog.dobryslownik.pl/galopem-do-muzyki-a-to-ci-opera/
Unfortunately, Vengir's link to the word list doesn't work any more. Maybe it has moved to another place, but I can't find my way through the Polish Wiktionary...
An interesting fact is that all the words listed here by Emwue are loanwords from Latin or Greek, while 'papryka' has a Serbian origin.