I'd just reconsider, and stop this - it'll only cost time and money.
I think you got a fair deal from the CAA. You did get a free retest. If you did get your result "converted" to a partial pass, which is the best you could hope for considering there were other issues in the test, you would have to pay half the test fee for the re-test, which is not miles off the cost of the aircraft for the first test. Also, you did get some flight experience, so you could consider yourself the winner.
As some here wrote - I wouldn't know, not hiring pilots for a living - noone will care, there is just one more dual entry in your logbook amongst many.