Looks good. Some of those old irons can be worked with a file. You might try that first. Otherwise, you need a narrow enough grinding wheel to get into convex curve. If you do use a grinder, keep an eye on that tape just in case heat or water causes the tape to move. If you cut the tape as you mentioned, you might run a sharpie line along the tape, just in case.
It is hard to see how the previous owner made that plane cut since the profile is so far off. Big arms, I guess. It must have been a favorite plane because, as a guess, it looks like the profile error is just from a lot of sharpening.
Do you know about putting wax onto the sole frequently during use to reduce wear? I have a hunk of canning wax (you can find it in grocery stores and hardware stores in the US. Gulf is a common brand).