Alrighty–if you guys live 20 minutes away, my sympathy for him has just dried up completely.
**An ultimatum is bad–you don’t want to arm wrestle him into marrying you if he doesn’t want to marry you. Ideally, he should passionately WANT to marry you. **
The next time he mentions living together, you can tell him, “Sweetie, the ball is in your court. I would love to get married to you, but I don’t want to move in without marriage. Aside from the moral aspect, I have a child to think about.”
Be prepared to have him break up with you. Also, have a mental kill date set up after which (if there is no proposal), YOU break up with him--no more than six months, I would think. By Christmas, you should either have broken up and moved on or be engaged already. This man has taken up more than enough of your time.
I was in an even worse boat years ago - 2 years on a dead-end relationship with a guy who wouldn’t admit that all he wanted was a friend to hang out with and was not the marrying type and definitely not type who ever dreamed of being a dad, and I wanted several kids. After I broke up with him when I finally got a clue

uch: it came to me one day that in any future relationship, what I would do would be to evaluate in my own mind at approximately 3 months in whether I liked the guy, and whether he seemed to feel similarly about me. We might not be completely on the same page at that point, but if there were no serious red flags, I could stay in it and keep track of how it was going.
Then by 6 months, if no progression toward commitment occurred, we would be having the Serious Talk. It would be calm and I would be prepared and tactful, and if breaking up proved necessary, it would be much less painful for both parties after a shorter dating period. (Also, getting back together later could still be on the table depending on the situation - but the break should still be a clean one for the time being, with neither party stringing the other along with false hope.)
I’m not sure, OP, if I’m reading your description the way you intended, but it sounds like he’s giving you mixed messages - he can’t wait for lots of time with you, but he can’t decide whether he knows you well enough to marry you. It’s confusing.

And I sense you may have your own doubts. Listen to them, find out what message they are conveying. It may not be to break up, but there is some message there.
Finally, the point of marriage is to help your spouse get to Heaven, and any children the two of you have, to do your best to give them what they will need to get to Heaven and then pray they hang onto it. This should be in the forefront of each party’s mind.