Not sure if this would help Jonathan, but it kind of reminded me about a user who used the 'clearable' alarms.  Under normal circumstances, when the alarm condition is no longer valid, an alarm clears and disappears from the Active Alarm list.  With the clearable option, the alarm would go into a clearable state (and stay visible in the active alarm list, showing green to indicate that the situation no longer applies), and the operator has to manually clear the alarm (change it from clearable to cleared).  This is an option used by operations that want to make sure that nobody can ever say that they did not see an alarm, because it has to be manually cleared by somebody.  Not sure if this would be of interest for your case.

Locking the Alarm Console so that it cannot be hidden is not available.  Then again, is that a guarantee that somebody will see an alarm?  Would the banner notification option maybe also be of interest?  So that a new alarm is always visibly announced in the header op Cube, even when the Alarm Console is minimized?