Firstly, please quote the case reference number in your final letter.
Secondly, whilst I understand why you are taking this approach, you may be leaving yourself open to a high cost. For example, if the TOC says it wants a £500 admin fee to settle, given that you have said that you want to pay to clear the issue, would you be prepared to pay this much? Can you then turn round and say you don't want to settle after all because the cost is too high?
Would it be sensible to suggest that you would be willing to pay £50 towards their costs? In that way, you could back out if the admin fee was too high, and that may also then set a limit for the costs element, given that they should know that they can't threaten you with Court action.