Thanks for your full response.
This sounds like a reasonable position for the employer to take - and on that basis I would agree that the whole cost of the course could be claimed.
I have added a link here from the employment income manual that details when those costs should be apportioned
This clearly was not a reward for you, and based on what you advise it was directly linked to your employment at that time (and continues to do so) and has tied you with that employer for 4 years, so they benefit from the training you have undertaken, which further supports the position.
And the purpose of the 15% you paid (and the amount you were out of pocket) was to show your seriousness to the course and the employer, rather than because there was an element of the course, that would not benefit the employer, or was not employment related.
And if you are happy (as is your employer) to accept this was all related to your job at that time, then HMRC should not have room to disallow the full claim.