Note that you cannot get DZ pre-approval auth if the area has LAANC. IT will tell you that LAANC is available and to use that.
When you get that "noification" you can indeed keep going in the Drone Zone and request a higher altitude. In fact, there is an excellent post going on with detailed instructions about this over in the Commercial Drone Pilots group:
COA for flight above LAANC altitude
What is the proper procedure for requesting clearance to fly above the LAANC altitude posted on the FAA UAS Facility Map? I have submitted through the Airhub app multiple times for various jobs. If you request clearance above the published altitude it says 'Requires Action - Further Coordination...
commercialdronepilots.com