C/D/S/D: Minutemen

I haven't heard a great deal of Parquet Courts but they seem like something that would about fit the bill. Also White Denim

> I know it's essentially a question without an answer:

I think it's not even possible without the fourth Minuteman: President Ronald Reagan.

> "but still has a similar sense of groove?"

But for the death-before-midrange and jazz sympathies between the players, this Kurws album comes the closest for me:

https://kurws.bandcamp.com/album/dziura-w-getcie-hole-in-the-ghetto

This is probably cheating but Big Walnuts Yonder:

https://www.youtube.com/watch?v=6bfraz58MpI

Nick Reinhart, Mike Watt, Nels Cline, and Greg Saunier