Quantizing confusion-please help!

Im DESPERATELY trying to replicate the basic drum pattern from a song by a band called ‘The Beautiful South’-the song is called ‘Rotterdam’ (easily found on all popular video viewing sites)-its a simple shuffle using brushes on a snare drum. I can roughly play it into cubase via midi keyboard and a drum plugin-BUT for the life of me I cannot figure how to then quantize what I have played to get it properly in time. No matter what settings I chose, whether 16ths, or triplets, auto, etc-the drum hits never fit to the marks on the grid (and I’ve tried adjusting that too), and the beats are never quite in time with the 4/4 click. PLEASE help!!!

1/8T - But that track sounds like a drummer played on top of a loop. You can hear flams randomly throughout the track.

If you listen to the first half of the bar when the drums start it’s just drum programming. Then on the 3 of the first drum bar you hear either a real drummer or a loop kick in.

So there could be a variable which might make that looseness illusive at first.
A strictly quantized version of this would sound homogenized relative to this recording.

My advice would be to experiment with some loops that might be derived from human performances. You might get lucky with that loose semi sloppy vibe.

Or set up a basic track with a light kick, brush snare and tight maraca (on the triplets) then ask a drummer to play in some triplets and random fills for you on brushed snare. Then add some tambs scattered tastefully and you should be 90% there.
I’m pretty sure that’s what Beautiful South did.