I think that you are on the right track with a fast-twist barrel. I would recommend 1 in 8" or possibly even 1.7" if you wanted to shoot something like a Hammer Hunter in 168gn.
Once you have the twist and barrel the rest is according to your wishes.
[If you had wanted a standard round, then the old 270Win or 270AI would be great and would not raise recoil. But you might as well use the magnum bolt face.]
Frankly, .277" bullets don't recoil very much (said by someone who hunts deer with a 338 and plains game with a 416 or 500). So some of the extra capacity rounds are worth considering.
The 270WSM and 6.8Western are almost the same round with different factory twists. The WSM comes with 10" twist, the 6.8 comes with factory twists of 8" or 7.5". If you are putting on your own barrel, then these are virtually the same round. (Technically, the 6.8 is 0.08" shorter in the body, the shoulder and neck are absolutely identical, as is the case head.) I would go with either round if desiring a short-action load, although the 6.8 is more adaptable for longer bullets in a magazine. I would also discuss the throat with your gunsmith, since you could put in a sloping leade with a custom gunsmith. See SAAMI diagrams below. Note the sloping leade in the 270Win, and the 0.1" freebore in some and the 0.38" freeborn in the Weatherby, excessive in my opinion.
If you want a longer action, then the 270 Nosler would make sense, with 15 grains powder capacity over the 270 Weatherby. It's your call.
In terms of powder capacity, listing short action to long, your choices are:
75 grains (6.8W), 79gn (WSM); 67 (270W), 70 (270AI), 81 (270Wby), 95 (27Nos).
But again, study the throats and discuss with your smith:
270Win
6.8Western
270WSM
270Wby
27Nosler
Personally, I would replace the Nosler throat with a traditional 270Win throat. The 0.1" freebore are fine as is. With long mono bullets you might want a 0.1" freebore put into a long sloping 270Win throat, if given an option.