I have the Titleist Lightweight Cart Bag (14 way divider) and this is my third one. I have always used midsized GolfPride grips on my clubs Driver thru wedges and have never had a problem with the bags. I am on my third bag. I use the oversized 140 GolfPride grip on my scotty. I also have two other bags: a tour bag for tournaments and special events and a lightweight carry bag for travel. I find that the Titleist bags are accommodating.

I had the same issue, went to a staff bag. I think it has 8 areas, and I used those tubes in them. Works for me. Hit um straight, Dave...

I currently game mid size grips on my irons and have the midsize staff bag. The bag has plenty of room for the clubs and there has been no signs of wear on the shafts from being in the bag.
Hope this helps!
-Greg

I also have the AP1 clubs with graphite shafts, vokey wedges and S. Cameron putter with fatso grip. All clubs mid size grips. I purchased the Titleist Stadry waterproof bag with large putter well. Awesome bag easy access and lightweight.