OP, he doesn't want to marry, you, if he did you'd be married already.
And if you are working less than full time, have your name on the house deeds/tenancy agreement, you are definitly vulnerable.
I left my ex after 30 years and 2 DC. Wasn't married because I bought his bullshit that everything was great and no need for marriage.
I am now having to rent, and money is tight, because of my rose tinted specs. Things are changing, but that was due to luck and nothing else.
Marriage is a protection for most women because it's usually the woman whose career gets shafted after having children, especially if the woman is SAHM. She is financially vulnerable and that's no place to be if she's the one who will be the primary carer.
So, OP, I reckon your DP is trying to string you along. After all, marriage will not be an advantage for him. He has a "wife", a child, a home life, food, laundry, etc sorted. Why would he want to get married and risk his assets?
7.5 years? He'd have married you by now if he wanted. You're not his Miss Right, just his Miss Right for now.