The asteroid-go-round (AGR) would not solve the problem of delta-v (change in velocity) needed to match the speed of the hydrogen carrier to the speed of the AGR. Even if the AGR gets very close to Jupiter, it's still whipping by at a tremendous speed. If the hydrogen container is somehow lifted to orbital hight, it's still left unmoving in the path of the oncoming AGR and wham! oops, there goes all your hard work. To accelerate a large mass of hydrogen (or anything) enough to move it away from Jupiter and toward somewhere else, whether it's carried on an AGR or not, still requires the same amount of energy.

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"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
"The Mayan symbol for "book" looks a lot like a triple hamburger, but I've never seen them claiming it as proof the Mayans had Big Macs." - KaiYeves
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort