For your P1 you would have two clocks running rather han the one it sounds like you have. The first would measure from when the process was opened to the status in your process which means 'responded' in that process. Your second clock would then probably also start at the same point, but would be completed when the process was resolve.
I agree with Dave on having both "Response" and "Fix" escalations (clocks) running against each Response Level as this allow you to have different notifications etc during triage.
Another way to look at this though when combined with Self Service is that is doesn't matter what Incident is logged, they should all be triaged the same because until you've read the description, how can you determine its importance. Combined that with I'd communicate (on the Self Service Window/portal) that is the user thinks it's a P1 or P2 then pick up the phone and call the Service Desk! Therefore IMHO all Incidents should be triaged with the same "Response" escalation whether it be 15mins, 30mins, whatever. So more recently I've been creating the main Response Levels with just a "Fix" Escalation (clock) but also create an additional "NoSLA" Response Level which is set by the system for Self Service logged (email or Portal) lifecycles. Then at Triage status the Analyst changes the "NoSLA" Response Level to the correct one and the escalation points recalculate. For a Analyst created Incidents you wouldn't see this option as it wouldn't be in the SLA matrix setup but that doesn't stop Self Service or Email setting it. The advantages is you have a less complicated setup on Response Levels as only have the "Response" clock in one Response Level to configure. It also makes it more obvious to the Analysts triaging that they need to change the SLA; the alternative is that you set a middle-of-the-road Response Level on creation from Self Service and the Analysts then can fail to change to a more appropriate value.
My two-penneth worth anyway! :0)