THAT is the trick!! Never thought of it and it never occurred to me that they would be looking only for the numbers after the leading 157. Other airlines do it where they prefill their airline-specific code, in this case 157, to let people know that they only want the numbers coming afterwards.

I now did exactly that: ticket number without the 157, for four claims. They show as "approved" already 30 minutes later. They are not yet reflected in my overall balance, but I assume that will happen after they've run their IT update.

Thanks a lot, learned a lot + solved my problem.

By the way, of all the airlines that I use I find Qatar the least reliable when it comes to crediting miles.