2.5 cm shorter chainstays will definitely make for a quicker-handling bike, albeit less stable. Also keep in mind that the Vaya climbs poorly because it is likely a ~25 lb steel bike. My ~24 lb Space Horse does not climb anywhere near as well as my ~17 lb CAAD9. I believe most of that is due to the significant difference in weight, as the Space Horse is actually much more stable climbing (due to the more relaxed geometry). On flat ground, there is only a marginal difference in speed between the two bikes (when they are both equipped with 25c tires).
I'm betting the frame weight on the DCD is pretty similar to the Vaya - the DCD is made from basic mid-grade steel, fairly similar to the Vaya (there is just less of it). So it is possible that climbing may not improve as much as you think in switching to the DCD.
If you really want a quick commuter/gravel bike, you may want to get something lighter. Consider a carbon/aluminum bike - I would actually look for a CAADX cross bike, due to the rather light weight and lower cost. Or, even something that is fully carbon fiber (if you can find it with disc mounts). Another weight-reduction option is cantilever brakes - it doesn't rain much in Austin, so discs are non-essential unless you ride often on muddy singletrack. Discs require more frame material and a stiffer fork - not good for weight/handling. Disc wheels may also be heavier than comparable rim brake wheels, which increasing rotating mass (leading to slightly worse climbing and acceleration).