Well, it would be interesting to take it apart and see if the race is indeed loose. What I've seen a lot of times is mismatched headset components. A lower cup from this headset here, an upper cup from this other headset, and a crown race from yet another headset. The shape and curvatures of the cone doesn't match that of the cup and the ball-bearing isn't located properly and things slide around, even when all the individual components are tight on the bike-frame and fork.
Sure, cleaning off the mating surfaces would help the JB weld adhere, but we don't really want to do that. You'll never be able to remove that race again.
The JB's really used as a gap-filler, but I'm not how strong it is in compression. I would mix in some powdered metal filings to add some compression-strength to the JB. You end up with making another product called "Liquid Steel" or something like that, I've used it to fill 1/2" holes in motorcycle cases and it actually works very well.
So you can apply your glue-mix to the seat on the crown first, then slide the race all the way down and press it as far down as it goes, don't pound as it may jar it sideways too much. Then let sit and harden over night.