Unmarried partner visa - need advice on cohabitation proof.

Hello,

My partner (EU national with settled status) and I are trying to apply for the unmarried partner visa for me. He meets the financial requirement. We've been living together for almost 5 years. For the whole time we rent a whole flat by ourselves, meaning that the lease is under both of our names, and our names only (mentioning this because a lawyer I contacted said this might be helpful in proving that we are in a relationship instead of just roommates).

But a serious issue is: Since I have been studying and not working full-time (so don't have much money), he has been paying all our utility bills and council tax by himself to be kind. This led to the fact that those bills are all only under his name. We don't have documents to show that we have shared responsibility.

The only proof of shared financial responsibility I can find is I always transact half of the rent to him every month, which can be seen in bank statements.

We only got a joint account less than a year ago, and that's because his families suggested as a couple we should share one of those... If that can more or less help.

What we do have is plenty of documents and official letters addressed to only one of us, like GP letters, tax letters, phone bills, bank statements. From my research, although they are not as important, these can at least count as proof that we've been living in the same address over the last few years.

Now my question is:
Based on my situation, what's the best way to gather a convincing set of proof for 'cohabitation in a relationship akin to marriage'?
We don't have plans to get married any time soon.

Thank you.

Some further info and questions regarding our council tax situation:
After some digging, we found that my name is not on the council tax bills, but it was written in the bills that we got a student discount for council tax. Would that be proof that I'm at least included in the council tax account of our household?