Wow. And you are an instructor no less?
You got the 50 feet climb performance required to establish the service ceiling. But my friend many many other factors involved. Like weight and temperature. We have on average a plus 15 to 20 ISA here in the mid latitudes. Full of fuel, high temperatures. A sudden and dramatic drop after reaching 45,000 feet. Come on, you are better than that
Yes, I believe that if the aircraft climbed to FL450, under the conditions you outlined, that at an altitude less than 2,000 feet above the service ceiling, the plane would not stall.
The smallest plane I have flown over it’s service ceiling is a Grumman Cougar light twin. The largest plane I have flown over it’s service ceiling is a Cessna Citation. Neither airplane was near a stall. The Citation was at about .6 angle of attack.
I doubt it was ISA +15 or 20 at FL450.
In summary, I’ve done it.