I’m on the sunny uplands: I got there by only cold-solving about half the clues, then starting the grid fill and cracking the enciphering so that I could back-calculate to give me hints for the remaining clues — but I definitely had, and heavily used, a searchable Chambers app. The enciphering would have been tough to crack without it, and several of the words that result are quite obscure. Good luck!
In fact, so reliant on my searchable dictionary did I inadvertently become that I started to think I had made a mistake when two of the words would not work out: I eventually got plausible-sounding words but they just weren’t in Chambers. They were 23a and 29d. Then I remembered the preamble :-)
You’re guess is inspired: stick with it. And your partials are good too: you need to do more of that. For example, where 9a and 5d intersect you should see that K = E? and that means that the enciphered 9a looks like ?E???E??E?. Feeding that into my search finds 159 matches: still a bit too many to work with, but we can do better...
Similar spotting of pairings shows that F = X?, O = ?X and L = X for some as-yet-unknown letter X, and this gives some real structure to our 9a: not only does it have the pattern above, but also the first letter matches the fourth and fifth letters. You could try some guesses for that letter X. But this is where I looked down the list of 159 matches to find any words in the list whose first letter was also their fourth and fifth. There was just one such word. Fed into a 13-shift simple Caesar cipher that word would be erneerfgrq. That then fills quite a lot of grid cells, and provides the first and second halves of quite a few pairs. Continue like a codeword puzzle and it should eventually unfold nicely.
A searchable dictionary really speeds that final enciphering solve up though. For example, it shows that ?te?a has only one match in Chambers, which is fgryn on the same 13-shift. Many other letters fall to “there’s only one word like...”, which inevitably becomes a bit more supposition and checking, however good your knowledge of the BRB, without a search.