Your mount doesn't come apart like this Nikon M-223 mount?
I am surprised if it doesn't. I thought that was how pretty much every Weaver/Picatinny mount worked and it would be odd that Nikon had 2 different designs. 2 screw vs 3 screw.
I think I would just get another scope mount before I would start swapping BUIS. You can get a Burris PEPR mount (I just got one from SWFA) for $69.99 and you CAN take those off.