Manual IPL is a start.
<i>I do have access to other DST profiles and can access SST…</i>
That indicates that you created at least one additional *SECOFR profile, which should have been one of the first things that was done on the system. QSECOFR ought to be used extremely rarely — ideally only at IBM’s direction in order to minimize risks and to avoid situations such as your current one.
With a *SECOFR profile, use CHGUSRPRF to set the QSECOFR user password if that has been lost. Once you can do a straight logon with QSECOFR, you have a good chance of getting through the rest.
Sign on with QSECOFR using the new password. Then run CHGDSTPWD *DEFAULT. Review the help for it and see if it gets you on your way. Note that CHGDSTPWD may be available for your other *SECOFR profiles. The default DST password should already be known to you — and remember that it is upper-cased.