Hoghead,
What it sounds like is you want to use same action / bolt (.473) and possible reloading components. If the 6.5-06 isn’t doing enough for you you have 4 options I see: 6.5-06AI, 6.5-280AI, 6.5 Gibbs, 6.5 Sherman.
I have a 6.5-06AI and it shoots great. In a 26” barrel I can get the 156 Berger up to 3100+, but settled on a node at 3030fps that shoots .52 MOA out to 500 yds (furthest I’ve taken it). I haven’t focused much attention to monos in it. I did pick up a couple boxes of 122 grn Controlled Chaos just to see how they shot and they’re very impressive.
Out of all the above listed cartridges a 6.5-280AI would probably be the easiest. Just find yourself some 280AI Peterson brass, pick up some 280ai bushing dies and a .290 (ish depending on neck thickness) bushing, neck down to 6.5 and feed her.
Good luck with your decision and let us all know what direction you go!