If both motors run fine with a different esc and one delays with your new one that would indicated something with the new esc is effecting the motors, it could be the 'delay' from neutral to reverse, i know the mtronic esc's have a 0.5 second delay time there, you will want to check your settings to full forward and reverse with no delay to eliminate that problem.
Have you suppressed the motors at all? this could be worth doing. apart from that try another motor where the one that is delaying, and see if the problem vanishes. if it does that indicated that the motor is going bad, if the problem persists then im out of idea's apart from using a larger esc (20A).
What size is your tug? 300 motors are quite small for a tug i would consider upgrading to 400's if you have the space, or if the motors are about to die!
Inherent problems with using 1 esc for 2 motors i think this is a common problem not just limited to you, i have always used 2 esc's and a mixer for twin motor setups, so never come across this issue to deal with ...
is the delay that long that it effect the models performance in anyway? i doubt it will make any real diffrence with a delay, worse case is the model steers a bit one way when throttle or reverse is added...