I would cut the canvas without hesitation.
Let me add that I have a fire extinguisher and a knife at each bunk aside from the extinguisher mounted by the door and one placed on the picnic table.
Other safety precautions I take are to have a water hose hooked up to a Y at the campsite supply, because I turn off water to the camper at night. I turn off hot water heater at night and when leaving camper during the day.
(My pup is 17 years old).
What year is your trailer? iirc at least from the 2000 model year, it was mandatory for there to be at least 3 exits from a trailer, the main door plus two emergency exits. In the case of our popup both bunkends had an extra zipper that basically unzipped the hole end wall, the bunkers had an "Emergency Exit" cloth placard sewen above the zipper location and very brief directions. On the TT, there is the main door, the bike door on the front roadside and a rear emergency exit window.