I wonder if the new (closer) vets use a different brand of vaccination both this time and last time compared to your old vets? Is there a sticker in the card saying the manufacturer?
Insurance-wise, check your policy to be sure obviously, but as I understand it the insurance is only affected in that they won't pay out for anything related to non-vaccination ie if the vaccine is for cat flu and he is unvaccinated and gets cat flu then they wouldn't pay out, it shouldn't affect them covering other health issues. Riley can't be vaccinated any more due to his epilepsy but the insurance still covers all other conditions.
I think the general school of thought is that by Robbie's age they've built up immunity anyway. One thing to consider is that he wouldn't be able to go in a cattery if he's unvaccinated, luckily I found a lovely pet sitter who is a vet nurse who visits twice daily when I'm away.
Hope he starts to feel better soon