Whether you use "bad/badly" vs. "poor/poorly", I don't think there's much difference in this context. They both are grammatical and understandable here as "I still do not pronounce well".
There is a trend in American English to drop 'ly' so that something that acts like an adverb instead looks like an adjective. So
I talk bad
This is similar to saying
I don't talk too good
where 'well' the adverb is replaced by 'good' the adjective.
(which is classic 'ungrammatical' speech but is what people might say acceptably in a very colloquial/low register setting.)
One most likely would not use 'poor' in this context because it would really stand out as weird ('poor' in this meaning of 'not good' is not particularly common in American English).
"I pronounce poorly", "I pronounce badly", and "I pronounce bad" are all fine in AmE, the last one not so much only because "pronounce", as a more technical word, is of higher register than "bad" and so it sounds incongruous.