Replace a 8.5x2.5 with 9x3?

Knowing that bike design a little bit, I'd say the swing link is going to contact the shock body for starters. Bikes with simple single pivot designs and no linkage are about the only ones that can occasionally accept that big a step-up in shock size. The older Bullit would accept shock sizes from 7.5 all the way to 9.0 inches only because they had no linkage, no stiffening link, and a two position shuttle...and the ability to remove the shuttle and bolt the shock directly into the frame. That is a rarity.

If there was no clearance issues, a 1/2" longer stroke would gain about 1.5" of top out travel with a 1/2" longer shock eye-to-eye mount (bottom out travel tire to seat post clearance would remain unchanged). The longer shock would raise the BB and sag nearly 1 inch using the same spring or shock air pressure, and the frame angles would be about 1.5 degrees steeper, making steering far quicker. And your seat and bars and rider weight would be further forward over the wheels and pedals similar to lowering adjustable fork travel on a bike by 40mm.

Even if you softened the shock and increased sag a lot, I doubt if you'd like the added braking dive from rear end rise with such a huge increase in rear negative travel.

Yeah, that's going to dramatically heighten the rear end too. I'm currently experimenting with an 8.75 X 2.75 5th E coil to see how it affects my Nomad's geometry. The Nomad shock is normally 8.5 X 2.5, so I'm only increasing shock size by 1/4"...half what you're looking at. This is quite noticeable on my Nomad, and I'm even running a 650B taller front wheel/tire setup.