Work Permit to Unmarried Partner query

I'm currently on a Work Permit Visa (sponsored by my company), and am coming up for my 2 year renewal, but wanted to explore the possibility of changing to the visa that allows me to stay in the UK as an unmarried partner - firstly is this possible?

My partner (British Citizen) and I have been living together for almost three years, but I'm struggling a little with the documents to prove this - as we have always lived in share houses. For the past year, we will be able to use the house tenancy agreement, but beyond that, haven't had utility bills registered in our names - but have had rent transaction between our bank accounts (will this count as evidence?).

Looking at Section 6 of the application and the documents listed - we have hardly any of those, and definitely not in our joint names (purely through the reason that we are living in a shared house of generally 4-6 people). So we will have to fall on circumstancial evidence - eg. Bank statements, pay slips going to the same addresses - will this suffice?

What other evidence can we use? - photos? transactions between our bank accounts? -HELP!

Also just regarding my status - I have been in the UK since 2002 - 2 years on a Working Holiday permit, then almost 2 years on a Work Sponsorship permit (up for renewal - but another 3 to go, before I qualify for ILR) - whereas is I change to Unmarried visa - am I eligible to apply to ILR in two years?

Looking forward to any advice!
Thanks