Hi Andrew - a simple problem with a simple answer - your secondary throttle link disengage latch is seized in the active position. (Closing the choke flap operates a spring loaded latch to deactivate the secondary throttle butterfly)
Using photographs of one of my rebuilt carbs I will try to make things clear.
In the above pic,
A = the primary throttle shaft
B = the secondary shaft
B1 = secondary throttle adjustment stop screw
C = choke cam
C1 = choke on throttle progression adjust
D = secondary throttle deactivation sprung latch
D1 = latch spring (note retracted position)
E = the link to the secondary throttle
With the choke in the open position, opening the primary throttle causes the linkage to connect with the sprung latch and operate the connecting link to the secondary throttle
Further opening the primary throttle causes the secondary to follow

With the primary throttle fully open you see the secondary throttle has also fully opened
In this pic the choke flap has been closed and the choke cam has activated the sprung latch - note the spring is now in the extended position (much like the seized latch on your carb)
On opening the primary throttle the linkage bypasses the latch and the secondary throttle cannot open
As for the hole in the primary butterfly I can only assume that it has been done to bypass a non functional idle circuit. The carb is designed to idle with both butterfly closed with the idle mixture entering the primary venturi below the primary throttle plate via the idle circuit passages (which also has the idle shut off solenoid in circuit). Drilling a hole would allow air to be drawn through the closed plate carrying fuel from the main jets thus allowing some sort of idle. If the idle circuit and solenoid are fully functional I can see no reason whatsoever for the hole. (Solder it up)
The float chamber can be cleaned by soaking overnight in either carburettor cleaner or white spirit followed by agitating with a stiff artists bush or wooden "toothpick" - the chamber and all the various passages should be blown out with a high pressure air line.
In truth rebuilding a carburettor is one area in which a degree of expertise and knowledge is needed - if you have further questions please ask.
I hope the above is of some help and wish you the best of luck.
Mac.