Quietly going through these suggesting 'more slowly' etc as viable alternatives. I can't explain why but 'more slowly' strikes me as more grammatically correct than 'slower'.
'More slowly' did seem apter to me than 'slower' in this case. It could have been because I felt that 'slower' is the comparative form of the adjective 'slow', while I felt the comparative form of the adverb 'slowly', i.e. 'more slowly', should have been used here.
However, on further reference, it turns out that 'slow' can also be used as an adverb. Therefore, this sentence is grammatically correct.