So, of course we know that all relationships didn't start out the way you're going about things. That said, I think your ideas are actually quite sensible, which if I understand you correctly, go something like this:
Discuss early on what you're both aiming for, which you did. If, for example, some guy had said he's not at all looking to get married, you'd have known to stop right there with him, instead of wasting your time and emotions on someone who simply doesn't want the same thing you do.
If he says he is looking for what you're looking for (and his actions seem to back up his words) then date each other for around three months with no commitments to each other, to get to know each other a bit before proceeding to a more serious step, which is where you're at or approaching now.
Now you're getting to the point where you've had enough time to know if, at this point, you both see yourselves ever possibly getting married to each other. I would give it the full three months because I feel like that's already a pretty short amount of time. But at about the three month mark, I don't think talking to him about where he sees the two of you headed now and about becoming definitely exclusive, will scare him off. Unless he's just not feeling that with you anyway. In which case, I think it would be smart to end it and be free to try again with someone else.
Of course you can only know what someone tells you, along with if their actions seem to match what they're saying. Also, three months is still pretty new so a commitment for now could still not work out long term. There's just no way around that, no guarantees, just clearing one more hurdle.
And of course, as nerve-wracking and uncertain as the process can be, it still wouldn't help anyone to try to short circuit the process of getting to know each other, then discovering if you're compatible for the long term. A look at the 50% divorce rate shows how important it is not to go too fast. I bet a lot of those people wish they'd "wasted more time" getting to know their now ex-spouse in the first place and "wasted more time" starting over again instead of settling too fast for the wrong person.
Some level of anxiety is very normal, in my experience. It probably just means you really like this guy and feel like he could be "The One." I do remember that stage, though for me it was many years ago. When you feel like you've found your special someone but it's simply too soon to trust that he will be your special someone for life.
So to answer your question, I'd go ahead and give it the full three months, then maybe start by dropping a hint or two and see if he picks up on it. Good luck!