Hello,
I have the same problem with a similar contract concerning a test of rt-10 hammer solid fuel engine in flight over kerbin.
I have managed to bring my rocket at the correct altitude and speed (not orbit... surface speed) and all the requirements are checked, but when I try to stage or click on the run test button (or even on the start engine button) the test is not accepted. I play on ps4 v. 1.14 and the game has crashed several times when I was setting the correct thrust and fuel using the revert function. Maybe there is a kind of bug... And of course, I have the good engine, not a similar one.
I hope it helps, not just because I'm stuck at that contract, but also because I love this game.
Thank you