OK, so after playing around some more with Windows 10, I THINK I have solved the problem.
If I play my videos with another player, like Media Player for example, the issue does not arise. I was using ffplay as my default player and this seems to screw up the input languages on the login screen (bizarre!)
So I've switched my default media player now and so far so good!
I put this on here in case someone else has encountered this issue. I know SendKeys is far from ideal, but I have a bespoke piece of software that relies on it to work properly, and I'd hate to throw away tens of thousands of dollars by switching to another software!