Right, calmed down now
So I got one of the other cyclists who knows his maintanance to have a look at it.
After a minute or two of looking at it, fiddling around with it, trying to work out what was wrong, he started laughing.
So, I was flipping the stem, then screwing it back in ...
... from the same side - to me - as I had unscrewed it to start with.
Which of course is now the other side!
So basically the reason it wasn't tightening up sufficiently when the stem was flipped, but was fine the other way round, was because I was screwing the screws in from the wrong side!
Hahahahhahahahaohdear.
It's fine now, no need for a new stem
Thanks everyone for your help!