Sorry, I didn't explain that very well, hypotheses - ignoring the letters in the preamble leaves eleven possible words for 24a, but accounting for them still leaves two possible answers. That means you have at least seven alternative words (there could be more ambiguities in other entries too, I haven't looked that closely).
Therefore, the likelihood of arriving at the correct solution without checking the letters mix must be quite slim (I only discovered my error by doing so - I'd used one vowel once too often and skipped another one entirely).