Tuning Bit recommendation - a little repair advice

[opus37]

I am restoring a very old helicon. I have an old straight tuning bit for it, but it is hard to get the mount piece in the right position with a straight bit. I'm looking to our repair guru's for a little help. I tried a Jupiter bit and that was too small for the neck. I measuring the opening on the neck and it is 0.649" (16.5 mm). On the original bit, the small end is 0.57" (14.5 mm). What bit should I purchase for this and where can I get it (them)?

[opus37]

I was thinking that the King bit would be the one to try because the size is large. Do the current "for sale" king bits have the one large and one smaller arrangement?

[opus37]

I checked the gooseneck opening to see if a standard American shank mouthpiece fit. It did not, so King is the likely choice. I will try to find someone with King bits to test before I purchase the bits. Thank you for the help with this.