Myke
There are 12 different user's manuals for K22 parts - you need to use the one that matches your exact part. If you have a part with HSRUN mode but you don't have it in the document it can only mean the document is not for your exact part.
Look at the very first page of the user's manual to see the parts that it can be used with - for example here is the first page of the K22P121M120SF7RM which is one that does have HSRUN mode:

compared to one that doesn't (K22P121SF5V2RM):

The K22s can be somewhat confusing since different K22 parts can be quite different and incompatible, matching more closely to other differently names parts types.
Since I don't use the SDK (I use the uTasker project as optimised solution) I can't say which routines to use for the SDK but I can show these:
1. The HSRUN mode prevails over warm resets so in order to ensure RUN mode when HSRUN is not wanted after a reset I use this:
if (SMC_PMSTAT == SMC_PMSTAT_HSRUN) { // if in high speed run mode we switch back to run mode
SMC_PMCTRL = (SMC_PMCTRL_STOPM_NORMAL | SMC_PMCTRL_RUNM_NORMAL);
}
2. When HSRUN is used the following is set before moving to the higher speed clock settings:
SMC_PMCTRL = SMC_PMCTRL_RUNM_HSRUN; // set high speed run mode (restrictions apply) so that the clock speeds can be obtained
Therefore, essentially to switch back to RUN mode you need to first reduce speeds to within RUN mode specs then do an equivalent to 1.
To step back up you need to do the equivalent of 2. and then set the clocks back to the higher settings again.
Regards
Mark
[uTasker project developer for Kinetis and i.MX RT]