Your work is technically very interesting neverthless I have some remarks.
1/ I don't always understand the claim that the Fitch Paradox threatens Anti-Realist philosophy.
If everybody accepts the Knowability Principle restricted to basic propositions,
it sounds more like a victory than a defeat for the knowability advocates.
It seems that what is threatened is more the capacity of modal logic to represent the knowability.
2/ In your intuitionistic frame, as you say in proposition 5.8, it is impossible to have
'A' and
'not K A' in the same world.
So the Fitch Paradox is avoided but the result is a very poor epistemic logic where you cannot express that some truths are unknown.
3/ more technically in the figure below the proposition 5.7
I don't understand what happens in the world
y.
You have
y Rk y ;
y Rk z ;
y: p ;
z: not p
but you have not
'y: not K p' .
Does it stand that
'y: not not K p' ?
It is very counterintuitive.
Else I wrote a dissertation on these points.
I have published a - maybe insuficiently technical - abstract on this website:
http://philpapers.org/rec/MARFPS