Thanks for the responses everyone
The head drum does spin freely and in fact at one point when I first tried it it was spinning for a long period, even though the tape itself wouldn't thread fully. Not sure why it's doing something different now.
I should also add that rewind and fast-forward aren't functioning either; getting these working is less of a priority but I thought I'd mention it in case it sheds further light on the problem.
I'm beginning to think that the problem may be the tapes themselves as they all have signs of mould on them; the one I pictured is typical (and they all are the same specific 3M type.) But I have noticed that with some it gets a bit further than others, though none of them manage to thread round all the way. Additionally, only the left-hand spool on the cassette turns; I never see any movement on the right-hand one. This makes me wonder if the point it's stopping at is the point where the other reel needs to turn (if that makes sense.) If I do try and turn the reels by hand then they move but there's a lot of resistance, considerably more than with a VHS tape turned by hand (but then again I'm not familiar with u-Matic so this might be normal?)
I'm wondering therefore if I should just give up with these tapes and try to find one that I know definitely plays in another machine. Although the problem with buying off eBay is that it's hard to know what you're getting and whether it's in any better condition than what I have already. If anyone therefore is willing to lend me a known-working tape (without anything priceless on it!) then that would be much appreciated.