Even if/though we couldn't manage without their help, I wouldn't ask them
The correct answer is "Even if" because (as I understand) only 'even if' can be used in conditional sentences.
Even if we couldn't manage without their help, I wouldn't ask them.
We didn't ask them for help, and we wouldn't even if the situation was utterly hopeless which indeed it wasn't.
Even though we couldn't manage without their help, I wouldn't ask them.
We didn't ask for help and we wouldn't do it, ever. They did help of their own accord (but we hate them anyway).
Am I right or wrong? If the second one is not grammatically correct, what is the correct way to convey the meaning of the second sentence?
Common mistakes at CAE (2017)
Page 43, Test 8 3.1