I tried the Clone functionality. It works "somewhat". Meaning if I define a service with (a) method(s) with the same name(s) as those that the TestSuite being cloned refers to, it indeed creates a new testsuite containing copies of the test steps (and these even including headers, assertions, etc.), so that would almost fit my bill. I could live with the effort having to define those methods beforehand and having to select one for each step, although that's very tedious, too.
But - and that's big BUT: for some stupid reason it does not copy ALL parameters. My calls have about 10 parameters each. For some strange reason about 6 or 7 of these are copied over fine but 3 parameters are always missing.
The names are exactly the same so I don't get, why these values are not copied over, as well.
But just randomly copied values are almost as good or bad as none, since one then has to double check each and everyone. :-(
This is so infuriatingly buggy and intransparent!