Not valid if you fly commercial like a warrier but try the following:
The average rate of climb to the initial optimum crz lvl will be the instantaneous rate of climb at 2/3, yep, tho third of that optimum altitude.
(Just in Case): Initial opt crz lvl 330; average roc to go there is the instantaneous roc at 22000 ft. So reading a VSI of 2000 fpm at that level, you'll know it will take you another 5 to 6 minutes to 330.....ATC obliging.
Now, if you find a dusty yellowed page folder squeezed between the two volumes of the AFM behind Sir's seat, check enroute climb pages in the Normal Ops section, and they will give you the infos you need (want) without having to go to FL220.
Cheers.