 
 My poor old physics intuition will be very surprised if these tiny
 masses, sitting very close to Jupiter, play any role whatsoever in the
 problem.   Or, to put it more technically, the extra "volume" they add
 to the phase space of possible capture trajectories is negligible.
 
 Jupiter is 2E27 kg, while the Galilean satellites are around 1E23.
 
 Also, as I said, the few references that I've looked at do not
 mention outgassing or breakup as important processes.  The important
 thing is a Jupiter-Sun-comet "reverse slingshot" that leads to a
 weakly Jupiter-bound orbit for the comet (at least a temporary one).