Fat guy needing help

Fat guy here, needing advice. I am a 350lb shrek trying to be more active and enjoy life more. I am riding a Specialized Roll with the factory 650bx2.3 Specialized Nimbus tires. I have to keep these tires inflated to 50ish psi to keep from feeling like I am riding on sponges, but they are still pretty spongie. These tires are nearly slick and perform poorly on the wet patches of my local paved trails. Last year, I took a pretty gnarly spill on a paved trail, where water washed over the trail, leaving it like slick riverbed rock.

I want to replace the tires to gain traction. While at it, I think it makes sense to also increase the width of the tire. I think I would benefit from the increased air volume to support my weight, and also the increased footprint for traction. These are the tires I am considering:

Surly Extra Terrestrial 27.5 x 2.5
Schwalbe Super Moto X 27.5 x 2.8
Schwalbe AL Grounder 27.5 x 2.6
Schwalbe Pickup 27.5 x 2.6

I was nearly certain I would buy the Super Moto X tires, until I came across the Schwalbe Pickup tires, which are designed for cargo bikes. At my weight, any bike I ride is a cargo bike. This got me wondering if the stronger casing of these tires would better suit my fat ass, even considering they are 0.2" narrower than the Super Moto X. Does anyone know if the gains from a more rigid casing would be greater than the gains from the increased air volume in the wider tires.

Any advice on my situation is greatly appreciated. Which of these options would you choose? Am I missing an even better option? I know this isn't bike touring related, but you guys know about carrying weight on your bikes, so I'd say it is touring-adjacent.

Thanks in advance!

My old man bike: https://www.specialized.com/us/en/roll-30/p/216878?color=349788-216878