I have a 1967 convertible Bird with a completely rebuilt 326 bored .040 over with stock cam and a Holley 4 barrel. I also added a rebuilt TH350 trans in place of the original Powerglide. I am looking to change my rear end gearing to achieve a bit more torque. I need to know if my 2.56 ratio XB rear diff will accept a gear change to 3.23 ratio. Further, can I use this axle and housing and turn it from an open diff to a posi rear?
Any info regarding this change and suggestions about parts is greatly appreciated.

You can use your housing. If you were just changing gears, then it would not be a straight gear swap with the series carrier you have without a spacer. If you are switching over to a traction lock carrier, then you will have no problems with the 3 series gears in it without a spacer. Auburn is one company that come to mind but there are others that make what you want.

I thought there were no aftermarket BOP posi units for anything numerically lower than 3.36. You might need to find a good used BOP Safe-T-Track unit for 3.23's

Great looking car by the way!

I did a lot of research on the posi kits when I did mine last year. Like Bob said, I could not find a 3.23, but did find a 3.36. I’d like to have a bit taller when I’m on the highway, but it’s a lot of fun on the back roads!

If you don’t mind straying from originality, you can buy an aftermarket chevy 12 bolt rear with pretty much any gear ratio you want with posi.

https://www.moserengineering.com/12-bolt-musclepak.item