I think there are probably quite a few options available to you. Have you heard of case collaborations? Because your topic of interest is related to your experience and work, I wonder if this could be an additional possibility for you. In case collaborations, part the funding is provided by a funder in industry and the other part is provided by a research council (as opposed to being fully research council funded).
This is the link to MRC case collaboration info:
You could also check out the ESRC one, as this is where the Psychology pathway is.
To address your specific question about a conversion course. I think it might depend on whether you feel you would benefit from it. I did a 1+3 which is a Masters + PhD. The Masters was an MRes which really skilled me up on the research side and was a great foundation for doing a PhD. The funding often includes this MRes year (at least Research Council funding does) and I would highly recommend it unless you quite confident in doing research already.
Do you have a specific idea already which is why you mention going down the psychology pathway rather than the medical one?
I don't think age really comes into it (expect for being an advantage due to your experience).
Hope this helps somewhat - there is a lot more specific advice that could be given about funding etc.
Ps. I am not sure if opportunities for next year are already affected by Covid-19. Again, you'd have to look at the Research Council funding websites for that info.