Knowing that backdoors exist to these products, are Chinese, Russian, and other Western intelligence organizations trying to brute-force calculate the location of these known backdoors?
If NSA opsec was such that an outlier like Snowden, ideologically motivated and willing to up sticks and lose a career and a nice untroubled life, could access and deliver detailed information on backdoors (we haven't seen any specifics, but indications seem to be that they are likely in the docs Snowden lifted) and cover his tracks, then it seems at least worth considering that "normal" spies, where the motivation is money, sometimes blackmail, who will stay in place or exit gracefully, have already delivered similar information to parties with the means to procure such, including the ones you list; so they might not need to brute-force anything.
The infamous Google/Gmail hack December before last was specifically targeted at an internal Google system designed to allow access by law enforcement.
At the time it was made to sound like it was used by conventional warrants, but it is pretty clear now it was probably mostly used by for FISA requests.
The (allegedly Chinese-linked) attack successfully penetrated that, and used it to access email accounts used by Chinese dissidents.
I don't think you can rule out the fact that they are not aware of such backdoors. If NSA can pay people to write such backdoor from time to time, other countries would have similar resource devoted to decipher the complexity of openssl (just an example) to find exploit. I am also sure this backdoor business is not new to the intelligence community anyway!
