You have to realise is the onus is on you to prove your suitability as a LAE.
One way you can do this is get the CAP741 and fill in all the training sections.
A military supervisor can sign off on this.
The more info YOU provide helps YOUR case. Yes people have been declined for not showing basic hand skills, this is entirely down to not using the log book.
Its their log book fill in the sections relevant and they can't complain.
1 year civil experience may be sufficient including your time in the military.