From what I can see on the schematic the trigger needs to be removed in order to remove the safety.
There may be a burr or rough spot on the trigger that is making it hard to move the safety. It could also be a weak trigger spring. To check the trigger spring hold the trigger as far forward as it will go and try moving the safety to the safe position. If it moves without a problem replace the spring. Also make sure there is nothing preventing the trigger from moving to the front. (dirt, dried grease, burrs)
Let me know how you make out.
I know how the safety works. Try pushing the trigger forward and then moving the safety. When you put the plunger and spring in it puts forward pressure on the safety. Without the plunger and spring pressure if relaxed. A very slight burr can make it hard to move.
The trigger prevents the safety from being removed. It needs to come out first, then the safety.
You are correct, there has to be something on the trigger or safety that prevents the safety from moving freely. It doesn't take much to make a part bind.
If you run into any problem let me know.
The trigger is pretty easy to remove. Take the gun down to the 2 sections. There is one pin that holds the trigger and sear in place. With a punch slightly smaller than the pin, drive the pin out from left to right. The trigger and sear should drop down enough to remove them from the receiver.
To reassemble you will need a "slave" pin. Use an old drill bit that fits through the hole in the sear and trigger. Cut it a little smaller than the width of the trigger. Assemble the sear and spring to the trigger, slide it into place and insert the pin. When you insert the pin it will drive the slave pin out.
I will check in later today and this evening, if you have any problem let me know.
Most safeties are not reversible, There should be red on one side showing it is in the fire position. This would go on the left side so when the safety is pushed over from the right it will show.
I am 99% sure the longer end goes on the left. When installing it align it so the 2 cuts in the back side are where the plunger sits. You should have a stop with the safety all the way to the left and to the right. If it is in backwards the plunger will only align with 1 cut and will not move. The flat is where the back of the trigger will fit into when you pull it. When the safety is pushed to the right the longer end will prevent the trigger from moving.
The reason I said most safeties are not reversible is because it will only work one way.
The only things I ever use to disassemble or assemble a gun is a schematic or my memory. I do not have access to assembly directions from Winchester or any other manufacturer. There is no need for it, knowing how something functions allows me to assemble it by just looking at the parts.
Use the trigger pin, not a nail, a few thousandths of an inch can make the difference between something working properly and not working. Tolerance's are extremely small on most firearms. If the trigger is sitting back .002" bec ause the wrong pin is in it, it will prevent the safety from moving.