I'm not LTN based, but I fly the A319/320 from there on occasion.
It should be noted that the runway turnoffs at Luton are not RET's (rapid exits) as they have at STN or LGW, but 90 degree turns, and have to be taken at a fairly slow speed.
So, if you are going a little fast for the exit, then a quick backtrack of the runway is probably the quickest way off. The A319 can turn on a sixpence.
The "brake harder" moment you mention was possibly the pilots overriding the auto-brake by applying pedal pressure themselves?
DH