Basically observe the absolute closest place the tire comes to any part of the rest of the bike. Roughly, if you increase the tire width the clearance will decrease by half.
Gatorskins ride relatively rough; try GP 4 Seasons as they are literally the same puncture protection layer with better rubber and casing.
An intermediate cost solution would be tubeless compatible wheels and nice supple tubeless tires like GP5000 TL or Vittoria Corsas (tubeless). Particularly if glass is the issue, you can run way less puncture protection with tubeless because sealant is very effective at sealing small punctures.
Cushier bar tape is pretty cheap, too.