I buy tire levers for tire removal. You can use the other side of your trim tool with the 90 degree angle to give you move leverage. Tire levers have a ridge to hook the bead of the tire easier. Love those patch kits. Everybody just wants to change the tube and waste the tube. I prefer a repair. If done right it won't fail you. Never failed me. Many many years. So many flats before I used sealant.
Do you like to bike at lunch or something? I noticed the bikes are at the shop and not at home. I wonder if you liked to bike in the wetlands of the old shop down south or up near town where you are at now. Personally I feel safer in town. People around in case something happens and less wild animals jumping out like snakes and things
You have removed the nut on the stem and that's great. Some people want to keep it and lock the tube to the rim. And I used to do that but the thousands of times of flexing the metal against the rubber chaffed a hole at the bottom of the metal stem. So always keep it loose. Or removed. You don't need it.
Now you are talking my language! I was a bike mechanic for years!! I like to set the valve stem at the beginning of the name of the tire and that way when there is a puncture, I know where to look on the tire for a thorn.
Now would have been a great time to put in some Slime or Stans sealant through the hole. Because presta valves are a pain to open to put it in. I had a hardtail rockhopper too. Old one. Golden yellow. Stolen. Anyways you can also use a tire liner which is a rubber and kevlar barrier to go between the tube and tire to help stop these things. Because not all tires can go inside out like that.