What you are calling "induced drag" is actually vortex drag (which is often incorrectly referred to as "induced drag" - so its not your fault)
Lots of books on aerodynamics use the term "induced drag". It isn't incorrect to use that term when using the simpler, approximate models of drag of a wing as a function of lift, things like C_D = C_D_0 + C_L^2 / (e * pi * A) sort of approximation.
The angle of attack (AOA) does not necessarily increase just because the wing is cut off and I would suggest it does not in fact. [and other explanation]
It does if you want to remain flying straight and level.
Let's take a plane flying along straight and level -- call this the original situation. In that case L = W, and (as an OK level of approximation sufficient for what we're talking about here) L = L_leftwing + L_rightwing, L_left approx. = L_right, and L_left = 0.5 * W, and L_right = 0.5 * W.
Let's assume you are flying at a speed where there is lift being generated on the whole wing span. What happens if you remove half the left wing? The lift that that portion of the wing is also removed. If you don't change any control inputs, the plane will roll left and start to descend because L_left is now less than 0.5 * W and L is less than W.
If you want the plane to remain in steady-state level flight (and not roll to the left and descend), you need to increase L_left to be 0.5 * W again, which means you must increase its angle of attack. As WWII planes are fixed wing, increasing angle of attack of left wing also increases the angle of attack of the right wing. The right wing would now have more lift than 0.5 * W, and the plane would again roll left, but start to ascend some. To compensate for this, you apply some airleron to reduce lift of the right wing (i.e., right aileron).
Now, the plane is not rolling to the left or right or ascending or descending -- we have L_left = 0.5 * W and L_right = 0.5 * W again. However, there are some important secondary effects. The left wing is missing a portion. The missing portion has no drag, so that part of the left wing's drag is reduced compared to the original situation. However, we had to increase AoA to increase lift on the remaining portion of the wing, to get that wing's lift back up to 0.5 * W, which increases induced drag (or vortex drag or drag due to lift or whatever standard term you care to call it). Perhaps overall, there is either no net change to the drag of the left wing, or maybe even a decreased drag from the left wing (like a clipped wing). If there is a decrease in drag from the left wing, left rudder will need to be applied to compensate, or the plane will yaw right. Also, we have right aileron applied -- generally that will result in some extra drag due to aileron being deflected. So, some left rudder might need to be applied for that, too. The end result is that there needs to be left rudder applied to keep the plane from yawing.
So, to keep in a steady-state level flight with half the left wing missing, compared to the orginal situation, you have a tiny bit more elevator applied, more right aileron applied, and more left rudder applied. We have less drag from the portion of the missing wing. We have a little more drag on the portion of the wing that is not missing (as lift there must be increased a little to make up for the lift lost on the missing part -- but this is probably quite minor). But we have more drag from the control surfaces (especially the aileron and rudder) that are being held in a more-deflected state compared to the original situation. Overall, I'd think that this is likely to give a net increase in drag.
If you clipped both wings, then you would likely have a net decrease in drag (as you don't have to keep control surfaces deflected to keep in steady, level flight), which is why clipped-wing planes are faster (until they reach situations where they need the extra lift from the portion of the wing that was clipped, like at high altitude).
This is all testable in AH, but I haven't done it. I'm just recalling that my top level speed in planes where I've lost half a wing seems a lot lower than when I am undamaged, and I'm recalling that I have had to keep aileron applied, or I'll roll into the damaged wing, and some rudder to keep the ball centered, all as I'd expect.