I am guessing this is the Newer T05 that does not have the black sleeve that the assembly slides into that covers the top of the trigger. The older T05 had this cover that held the top cross bar and the long spring in place. On the T05 make sure when you install the pins thru the receiver that the safety notch is not in line with the pin. If not it will bind and can break the safety fork bar.
DoNe plenty of T05's and the 2 screw mods. Never had a problem with them. The coverlets T05 I had the same issue. Cocked and locked but would not fire. PITA when the spring is compressed and the piston locked. It is correct that you can adjust the screws where the trigger will not latch and or not fire.
2 screw mods need to be respected. Also once set to your liking blue LT. On a brake barrel the I'll adj trigger is a barrel bender even worse on a lever gun for fingers if the bear trap fails. Also with the 2 screw mid spring work can improve the mod and trigger pull weight. Jmo