The man wants a "Super 6" and already knows all about "Overbore" and "Barrel-Burner", so let's stop the finger wagging.
I run in 6.5mm circles and have, against all unsolicited advice, progressed from 6.5X55 to 264 Win Mag, to 6.5-300 Win Mag and now to 6.5 RUM. I did it because I wanted it, not for someone else. I shoot perhaps 50 rounds a year, so will only get perhaps 25 years of fun out of them before I lose extreme accuracy, which is long after I will have been bored by them and moved on to something else. There are powders that work well with even "extremely overbore" chamberings, but they are naturally few in number: US869; 20N29 and the like. In chamberings like these, Retumbo is considered "fast".
Maybe you want to stick with a standard bolt face, but if not, why not skip to where you really want to be and try a "6mm Win Mag" (aka 6mm Atlas - it's ALL been done before)- a necked-down 264 Win Mag? I know it has that bad belt, but smart people figured that out long ago and it still works. If it must be based on the '06, then you've already pretty much answered your own question - 6mm-06 AI. If the 6mm Win Mag, 264 Win Mag (or 7mm Rem Mag) brass is easy to find, and dies for the 6mm Win Mag are easy and inexpensive: you need a set of 264 Win Mag dies (with the sizing plunger removed) for full-length sizing and bullet seating; and a 243 WSSM sizer for neck sizing.
Finally, it won't "need" an extra long barrel. All chamberings "get the most" out of themselves, the longer the barrel. If you "need" to get 4000 fps out of a 100 gr bullet, but need a 24" barrel for the situations in which you will be using it, only something along the lines of a 6mm STW and up can do that - maybe. A 24" barrelled 6mm Win Mag does not become a 243 Win because the barrel's too short, as some would have you believe.