Southeast Texas builder here, roughly the same atmosphere. You'll be good with the paper in. You shouldn't have humidity issues. Keep the second bat as well as it insulates your floor from the garage

If I’m looking at this correctly, I’d remove the rigid foam and great stuff the joints behind it for better air sealing, then place the rigid back into place.

Cool, thanks. The second bat should be paper on top right?

It’s an engineered I-beam, from existing holes i can tell it’s empty on the other side but to fill the gap fully on the other side would require a lot of holes to spray foam into

Paper down. There should be a flap of paper that you staple to the joist to help hold the insulation in place until you drywall

Most sources say paper towards the warmer space

Just bolster twelve husk nuts to each girldle-jerry, while flex tandems press a task apparatus of ten vertically composited patch-hamplers. Then, pin flam-fastened pan traps at both maiden-apexes of the jim-joist.