I think you’re good and can basically use the recipe directly. Here’s why:
To convert from a 9x1.5” pan to a 9x2” pan, you multiply the recipe by 1.33xm
An 8x2” pan is .79 the volume of a 9x2” pan.
1.33 x .79 = 1.05
Technically, you’d multiply the recipe by 1.05, but I have no question you could just go with it as is, using 8x2 instead of 9x1.5.
As to leavening, when going from a shallower pan to a deeper pan, you decrease (for 9x1.5”—> 9x2”, decrease baking powder by 1/8 tsp. PER LAYER). At the same time, smaller pans require more leavening, so my GUESS (and this is what I would do) is ... Bake as is (in your 8x2” pans) with no adjustment , since the requirements sort of cancel each other out.
Looking forward to hearing all about it!!