I'm thinking that starting at The Centurion Lounge in T3 (not strictly the G gate/G1), it's probably 17 minutes of relaxed walking airside from G back through T3/2/1 to A (0.8 miles?). Taking a fast pace it could be done in under 15 minutes. But you might get sweaty!

Exiting through security and walking from T3 to A to G, and going through security might take longer if the lines are long at G security. There's at least six minutes of walking, plus the security line.

Maybe using Clear would keep it under 15 minutes in total, but otherwise I'm not sure it's faster to exit and re-enter security.