If he's at FL280 and the controller is trying to climb him through RVSM airspace, odds are good that the controller will want to get him up to FL430 as soon as possible...and I'm not sure a zoom climb works too well when you're looking to go up 15,000ft anyway.

In a CJ3, which climbs pretty well at altitude anyway, beginning a climb at FL280 and VMo should allow a sustained climb of at least 1500fpm (probably more) all the way to FL430.

When traffic is an issue for climbing, I like to tell ATC what climb rates we're capable of so that they can plan their separation accordingly - no surprises for anyone and once ATC knows what we can do it usually allows us to get a climb clearance.