help with double time feel in part of jazz song

[I_am_not_a_drummer]

Hello,

I'm trying to mimic the drums in this particular song (Joe Pass's version of I had the Craziest Dream).

https://www.youtube.com/watch?v=KfOlCETFSDM

The song is at a very slow 70 or so BPM. During the second time around, the tempo remains the same but the feel is almost a like double time. You can hear the band pick up in the video I linked between 1min15sec and 1min20sec. I'm using James Stix with the Jazz Swing style. I've tried inserting a hats grid and played with that but i still cant really get close to this quick, energetic yet slow tempo playing. Would I be better off doubling the tempo in my DAW at this section? Should I try another style or drummer?

I should note that I only have the most basic paid version of Jamstix--no AIpak or anything.

Any help would be appreciated.

[Azimuth (Archive)]

The Drummer is using brushes. The XL Pak contains the Brush Kit so I'm not sure how you can solve this. To me it sounds like the Drummer just gets busier with the Snare brushing during the pickup section you pointed out.