a .243 with a Hornady "light magnum" 100 gr. SST would be a great round. I would prefer a 7mm-08 Hornady "light magnum" 139 grain SST. Another good round for you would be .308 with 150 gr. SST.
They all have a MV of over 3000 and still carry enough energy at 300 yards to do the job (ref. chart) http://www.hornady.com/media/Light_M...y_Mag_Ammo.pdf
As the 7mm-08 cartridge is not readily available at the local hardware store, the .308 or .243 would probably be best.
All three have the same cartridge size and have considerably less kick than the .270 cartridge.
While you don't "feel the kick when shooting at deer" you may have a tendency to flinch more when using a larger cartridge as you get conditioned to do so at the range. just mho.
No, I don't own stock in Hornady just think these are the tightest shooting rounds off the shelf.