Looking for an overdrive pedal for Tele into a clean AC15C1 (maintains chord clarity)

Hey guys. As the title states been looking for a light-medium overdrive pedal to run with my AC15C1 as my go-to rhythm drive. I mainly play alt-rock that combines dreamy clean tones with throwback to more gainy tones of 70s/90s.

The key here is I need a pedal that can send my amp into overdrive but not get flubby when playing barre chords. And while I know the AC15C1 is heavy on mids, I've liked the mid boost that I've gotten from the TS9 and Hotcake, but can't seem to get chords to sound clean and crisp. I also like the TC Spark I have but am using that more as a solo boost/EQ and feel like I could use something with more gain and tonal character for my go-to rhythm tone.

For reference I'm going for a tone similar to the first 5 seconds of My Love is Winter by Smashing Pumpkins.
https://www.youtube.com/watch?v=U6e4SGgMTbs

Some of the pedals I have on my list are:

BB Preamp/BB MB, Boss SD-1, Way Huge Pork Loin

I apologize for the long post. Any feedback would be appreciate as I haven't been researching pedals for all that long and am still learning. Hopefully I've explained my needs sufficiently. Thanks again!

EDIT: Thanks everyone for the great suggestions. I realized while the BBP-MB was good, it was a little too much gain for what I needed. And I've heard great things about the Timmy and would still like to try it someday. For now I ended up dialing in a low-drive setting on the Hotcake that satisfies my needs (Level - 2, Presence - 2:30, Drive - 10). The overdrive of the AC15 is just near impossible to beat. If I need more drive I run my TC Spark after to add a bit more gain. Like others I just needed some time to get used to the pedal.