As far as I can see, the 10 minute grace period covers you for the gap, and you can submit reps on that basis.
However, it being a hire car complicates matters, because if you submit an informal challenge, it will be rejected. London councils reject >95% of all informal challenges, because they know that most people then just cough-up to get the discount. So assuming your challenge is rejected, what will the hire company do when they get the NtO ? No doubt they'll just pay it and off-charge it to you plus an "admin" fee. So unless you can get the hire company to name you as the hirer on the day of the alleged contravention, you'll still end up paying.
You need to check with the hire company what they do when receiving NtOs, and also postal PCNs. At the moment, you have no legal standing in the enforcement process.