My friend wants my wife to be friends with his wife, but is forcing it in an awkward manner. [2 M/F couples, all early 30s]

Hi folks,
Our friend got married this last year to a girl we still don't really know. She's a nice person, but honestly we have only hung out a handful of times. I don't think she's particularly close to anyone in our group, they have been together total for 2+ years so you can guess how much we've seen her (not much)
Some of the guys in our friend group get together for board games at our place every week, which has been our primary in-person hanging out. Women are welcome, and my wife will join sometimes, but his wife doesn't really enjoy games.
Most of our friends are people my wife knows from high school, but they were all her friends first. We've been in town for 8 years though, so we're all close now.
He keeps hinting at ways to have the 2 of them hang out. Like suggesting that they hang out for a Saturday while he an I work on a project. He'll suggest things to my wife and to me, but we have no idea if she even knows about these suggestions.
I finally told him this after a brief text conversation:
Of course now he hasn't responded for a while, and I want to make sure I didn't push too far.
Another example is that one of the other wives was planning to come over one night to catch up, and he suggested that his wife come, too. My wife said OK initially because it was an awkward situation (group setting), but then texted after to tell him she just wanted to catch up with her friend.
We feel kind of bad at this point, because he keeps trying to insert her into various plans, and we sort of... bypass the suggestions.
We've failed thus far, as we've sort of been brushing these suggestions aside for a little while, but we've got to suck it up.
TL;DR

Friend keeps trying to set our wives up on friend dates, trying to get through to him that this isn't how friendships develop. How to make this clearer?
Follow up texts with help from this thread:

me:
me:
him:
me:
him:

Source.