VNAV will level off perfectly well even with a high rate of climb and catch any altitude restriction in the legs page or set in the MCP, it will just catch VNAV PTH or VNAV ALT early if the closure rate is excessive.
However if there is a risk of setting of a TCAS caution or warning due to traffic above then airmanship dictates you select V/S to reduce the rate of climb to less than 1000FPM.
The best way is simply to request high speed so the 220kt restriction no longer applies thereby reducing the rate of climb while you continue to accelerate under the altitude restrictions and reducing any chances of a TCAS event.
The usual speed restriction after requesting high speed these days is 280kts.
Last edited by SMOC; 16th Jan 2015 at 21:36.