It is unclear from your question if you want to do both the Z axis and the core as your first step or only the Z axis. But from my analysis, either will work. If I remember correctly, Ryan has said in other posts that using the Primo core on the Burly will work but that you lose some of the benefits. As for the Z axis, I brought the lower Z bracket for both the Burly and Primo into Fusion 360, and they align:
So you can use the Primo Z axis on the Burly. Note that the Primo uses a different size of bolt. Also the mounting system for the spindle/router is different for the Primo, though you can put a Burly mounting plate on a Primo Z axis.