It also seems that specifying what is meant by "q" and "dq" is critical, and this seems to be underemphasized in the texts (and perhaps in this discussion).
Let's explicitly write
q(U) = Net charge on upper plate
I = current out of the upper plate
dq(U) = change in the charge of the upper plate in time dt.
dq(W) = charge moving past a point in the wire in the positive direction in time dt
Then
dq(U) = -dq(W)
And
I = dq(W)/dt (as defined in the "yellow box")
= - dq(C)/dt
This means any postive charge added to the upper plate must equal the charge flowing "backwards" through the wire. Conversely, any negative change in the upper plate as it discharges is a positive dq(W) in the circuit.
If both of these are called the identical "dq" then it is now wonder that there is a sign confusion. Depending on which dq you mean, I = dq/dt = -dq/dt!
I think simply being clear in the notation for "dq" may solve all the problems.