Then if the new mount's firewall hole position differs from the original mount, remove or drill out the existing blind nuts, and epoxy in a "plug" made from a standard wood dowel.

Make sure the plug sits level with the firewall back and front... I normally make the front a bit longer and work the plug into position so it sits flush with the back of the firewall.
Once the epoxy dries I'll use a Dremel sanding wheel to make the front of the plug even with the firewall.... once done you can drill new holes as needed.