You don't have a countershaft brake, it would be seen in the picture labeled "right side bottom view" and would replace the flat plate PTO cover that is held on with 6 bolts.
The only thing it would help is when starting from a stop, as without it you either wait for things to stop spinning, or grind gears.
It does look like a push type clutch, as I think I can see the linkage is in the bottom set of holes, as it should be for push type linkage. (pull type uses the top set of holes in the clutch housing)
So, we have not solved why it is hard to shift have we?
Could it be you just need some practice? It took me several thousand miles to get the hang of driving mine. I would recommend starting to learn by using the clutch and double clutching, eventually you may prefer to not use the clutch, but wait a while before you try that.
Grigg