The 270-308 actually has a slightly improved version. It is called the 270 Redding. From what I have read Richard Beebe, president of Redding Reloading back in the 50s was one of the proponents of this wildcat and may have named it. It was first made when the 308 came out. It has a 30 degree shoulder and the article below states it duplicates the 270 win in performance.
The July-Aug 1990 handload magazine has an article on the 270 Redding.
Butch Jenson son of Bob Jensen (Jensen's Custom Ammo in Tucson) had one back in the 70s, might still have it. I remember Butch raving about its virtues in a lightweight SA rifle for coues wt hunting.
Here is a link with some load data at bottom:
Adventures With The .270 Redding. - Free Online Library
Author's name is not shown. He used a 22 inch barrel and got 3025 fps with a 130 Speer grand slam and 46 gr of Varget.
If I were making this wildcat I'd consider the 270 Redding over the 7mm-08. There are dies available as well as reamers.