It's not desperate to state what you want and expect from a relationship. He can then choose to agree with it or leave. Simple.
I would be very wary of having a child with him at all but I understand you love him and at one point he seemed to want it too (maybe it was just words, though, who knows how his feelings have changed since then?).
I was in your position a couple years ago with my ex of a similar length relationship, though I was only 27. We split. I'm not hanging around for years on end with someone who doesn't want what I do. And fertility only decreases.
I'd tell him it's time to shit or get off the pot, you want to get married (NOT engaged) within the next six months and start TTC a couple months before the wedding. Or if you're happy to risk not being married, you are planning to come off the pill so you can try to conceive as you both agreed you wanted to. If he doesn't want that that's fine, it's over.
You actually have a better chance of meeting someone within the next year, both being on the same page from the start and cracking on with kids than you do hanging around getting less fertile with a guy who just keeps pushing it back, seriously. Even though it's a risk you're at least taking control over your own life and have a chance at what you want. And if you meet someone and it's too late but you both want kids it'll be a relief to you to both be on the same page wanting, and can work together on IVF, adoption, donor egg, whatever it takes. It's better to be in a relationship both desperately ready for kids and struggling than wasting away the months with a partner who doesn't want it as you get increasingly desperate and sad.
Ever month that goes by now takes you further and further away from being able to meet someone and have kids. There will never be a better time to leave and meet someone than today. Time is ticking. Don't let this person hold you back, he could leave you in a few years and then it's too late.
FWIW I left and met my current OH a month later. told him second date I want kids in the next few years. He's as excited for them as me and we have a date set next year when I'm 31, him 27, to TTC (we've been together 18m only but both of our careers mean that's the best time). I can't predict the future, can't guarantee we'll make it, can't guarantee he won't turn out like my ex or that we'll conceive, but my goodness it feels amazing to be with a guy who points out cute babies in the supermarket and talks about our future kids and is excited about it. I could still be with my ex going nowhere with no date in sight and eggs getting older.
You are a grown up, you can take control now and you ought to. It's your life, if you want kids so much don't wait any longer. No man is worth letting go of having a family if it's what you want.