Just to note that I do not have this aircraft so my input is based on general flying principles only.
Few questions/suggestions. But first a statement: absolutely by no means use flaps to try and reach the service ceiling. That is NOT what flaps are for and they will NOT help!
But your stall comment together with the flaps question raises a question for me: are you properly maintaining the appropriate maximum rate of climb speed when trying this? Some people seem to think you should try and maintain something near the maximum rate of climb while climbing and continue to pull the nose up as you get higher and the rate of climb diminishes. As the aircraft is incapable of maintaining that rate of climb, the speed will steadily drop until you stall.
Note that the max rate of climb is specified typically at or near sea level and drops off steadily as you climb. By the time you get to the service ceiling you would be lucky to be at 250fpm.
The other question pertains to mixture. When you say “Mixture was at max thrust/power”, do you mean that it was at full rich or do you mean it was appropriately leaned for maximum power at that altitude? Note that this question becomes irrelevant if you are using auto mixture.
Cheers
Alwyn