I have a 6mm BullBerry Improved.
This is based on a shortened 30-30 case necked to 6mm, and Ackley Improved.
Best I remember this is how I formed the cases.
30-30 Sizing Die
7X30 Waters Sizing Die
25-35 Sizing Die
6 BB IMP Sizing Die
Trimmed the case to length. Could have been after the 25-35 sizing die.
Inside Neck Reamed
One Bad Looking Case when you are done. On the Box my data says 70 grain Ballistic Tip, 2930 fps
I would probably have went with a 223 Super 14 barrel if I were to do this one over again.
I have a 6.5X30JDJ also based off a 30-30 case only full length. Not nearly as much trouble to form cases. Good performance also.
A 6mmx30-30 AI might not be terrible. I would get ahold of someone with one first and see how much of a pain it is to form cases for it.
My vote is for a 223 barrel. Brass is easy to get. No problem with case forming. Reasonable performance. Reloading Dies are cheap. You should already own them.
If you decide a 6-TCU sounds good, contact me for a Die Set. I have a set of Thompson Center Dies (Hornady Duracrome) I would part with.