I have a 30-06 AI, with a 24" Douglas barrel. It started out at 26", so I have velocity numbers for both barrel lengths : 3050 fps at 26"; 2950 at 24". That was with the Swift A-Frame 180-grain bullet, and H-4350 powder. With the heavier bullets and the next slower burning-rate level of newer powders, you might get the velocity you're looking for - but I wouldn't expect that to be the case. You may be crowding it a bit with this cartridge.
With the 30 Gibbs or the Sherman, I would think you'd be pretty close to your stated goal. If I were doing it, I would go with the Sherman, mostly due to the neck length. Support from the builder is also big consideration, and from what I've read on this forum, you would have that support with the Sherman.
The case-forming process is a consideration, and one thing I haven't seen mentioned yet in this thread is the hydraulic forming dies for the cartridges that have the shoulders moved forward. I have never tried this, so I'm not the guy to ask about the matter. I'm just suggesting that this is available with the Sherman, but I expect that these dies are probably pretty pricey. Would you save enough on components to pay for the dies ? Maybe ………..
On the matter of shooting factory loads, consider this : in the 30-06 Ackley, every gunsmith out there seems to think he has a better way of setting up the chambering job in regards to headspace. When I first got mine, around 30 years ago, factory loads only fired about 50% of the time. I had to have the barrel set back and re-chambered to make the rifle work with factory loads, and/or fire-form factory brass without a headspace issue. I had been using the secondary shoulder process as a band-aid fix to get me through the first hunting season, and it works fine.
This is what you'd be doing with either the Gibbs or the Sherman, and for minimal brass working, I recommend getting an 8mm expander mandrel to push the necks out far enough to establish a shoulder for headspacing. When you neck them back down for the 30-caliber bullets, do it by feel. A slight crush fit that requires a little bit of effort to close the bolt is all you need. Others have recommended expanding to .338" and then necking back down, but I found that a mandrel for the 8mm diameter was plenty big enough. It's a little thing, but it's something.
In any case, if you go with the Ackley cartridge, and you REALLY want the capability to use factory-loaded ammo, make sure that you stress this to your gunsmith, because otherwise you may or may not have that capability when the rifle is finished. On the subject of fireforming, regardless of which cartridge you go with, it is often recommended that the cases be lubed before fireforming. This is not only un-necessary, but quite possibly unsafe. Do your homework on that concept before you try it. I stayed away from it, and was very glad I did - especially when I saw a 257 AI that had been ruined employing that method. As I understand it, the problem is that with these straight-walled cases, a lot of the pressure is absorbed by the barrel, because they stick tightly to chamber walls. When lubed, though, all the pressure goes straight back, and it's all bolt-thrust. This can be bad news. Good luck with your project. You will learn a lot about brass forming and loading with any of these improved cartridges. It can be either tedious, or fun - depending on your level of patience with tinkering.