I've not tried H/H on my WSM but I found that starting with 2 lit chimneys of charcoal on my 26" kettle got me well over 410°. Did you start with more lit coals? That extra heat might get more air flow which should produce more heat.
I don't think a 22" kettle has any more air flow capacity (size of vents) than the WSM.
You might try cracking the lid open a bit.
BTW, the high heat on my 26 was for the first half hour of a turkey (ala Alton Brown) and it did come out good.