Inlay or hotstamp? I think 7/8 will knockout the majority of hotstamps. We'll see. It seems an easy transition to switch to a 1" bit. Can't wait to see what @InIver comes up with.If you only plan to mill out the existing inlay, then a 7/8" bit won't work, for two reasons -- inlays are rarely exactly centered (so a centered drill bit won't remove 100% of the inlay), and inlays often "stretch" slightly into non-circular shapes (and a circular bit the exact size of the original inlay diameter won' remove it all).
To consistently remove the entire inlay and leave no ridge in the recessed area, a perfectly-centered 1" bit will be required (or a CNC setup, like @Gear has).