I would not put too much value in Chuck Hawks charts or any others for that matter! They are good "guides" but, there are too many variables to consider unless these values are with the exact same weight, style and barrel length for each caliber. Then, there is also the size of the shooter and the fit of the rifle to that person.
I have a light .308 and a fairly heavy 7MM RM, I shoot 150 gr. bullets in both. If I had to say which recoils harder it would be the .308!
Long story short, the .270 or the .308 would both be too much for a bad shoulder/ beginner! The 7MM-08 might even be too much. A medium to heavy weight .243 will kill any deer out to 300 yds. That would be my choice.