Now for the bad news. I doubt that you will find printed information for a 220 grain bullet out of a .308, they just don't work out of it. The .308 Winchester excels with a 165-180 grain bullets so why would you want to use one that can't be driven fast enough to make them effective at the usual hunting ranges.
If you still want to try some 220 grain bullets check out the Barnes Bullet site. They have loads for a 220 grain solid which you can use if you back the powder charge off by 10% and work it up but the velocities are still under 2400 fps for the loads.
I'm with critter on this. I've used a 308 a lot of years and tried lot's of bullet's. 308 works best for me with 165 gr bullet's. Handles 180's pretty well but above that the accuracy falle way off, I mean way off.
Where the larget 300 mags really shine is their ability to handle the heavy 308 dia bullet's.
I have always looked for ways to save money and gain skills. I have the firearms basics covered so I rarely buy firearms these days. But I do watch for bargains. Sometimes a little TLC with simple tools will let you bring an old gun back to life without investing a lot of money. One such find was a side by side 12 gauge marked “W. Richards” It is not from the fine English gun maker Wesley Richards, it is a cheap knock off copy probably made in Belgium about a hundred years ago...