Is "more poorly" an appropriate phrase?

The British National Corpus has 13 cites for "more poorly", and the Corpus of Contemporary American English has 83 (including 8 for "even more poorly" and 1 for "more and more poorly"). Google returns about 826k results. So it's obviously being used and understood. And, as J. M. points out, it's not ungrammatical, either. (Now, if you were asking for possible alternatives, that would be a different question.)

From a strictly semantic standpoint "more poorly" is acceptable. It does sound a bit akward, as you said. In your situation, "moor poorly" might be better stated as "less appropriately" or something along those lines.

Technically, it is not grammatically wrong, but just using the word "worse" is likely more straightforward and colorful. Compare:

He did more poorly on the test.

vs.

He did worse on the test.