I'd email them again in term-time with the offer. One other thing you could try (if you have a bit of time on your hands) is to apply for a PhD that starts during what would be your final year (you could try to convince them to postpone the start until the autumn). If you succeed great. You probably won't succeed but you will have practiced the whole application process, put in words your motivation for doing a PhD and you could ask for feedback. This way, you are well prepared for the main RC season.
Make sure you have a good chat with your referees early next term to tell them what you want to do and would you would like them to do.