The numbers are just the core size. A .600 doesn't necessarily mean that it's a mid-size grip. Putting a .580 on a .600 shaft will make it feel a tad thicker. If you want the Titleist grips, you could always build them up with tape to your liking. There are many different factors that go into choosing the right grip size.  

I prefer my grips a little thicker as well and simply use a couple of extra wraps of tape beneath the grip to get the thinkness I require.  You can do this with a couple of grips to test and see what thickness (i.e., how many wraps of tape) works best for you, then regrip the entire set.  It does not take but a wrap of two generally to build it up depending upon the thickness of the tape, etc.

Hopefully, the number on the end of the grip is actually .580, not .560. .580 is what Titleist generally uses as the stock men's size where .560 is ladies. A Golf Pride midsize grip is +1/16 of an inch thicker than men's standard. You will need 3 extra wraps of grip tape to build the Titleist grip up to this size. Make sure you use grip tape and not masking tape for building up. Standard masking tape is much thinner.