Having a single lock for many independent counts seems like a shame.

Indeed it is, as I would unnecessarily block an application which could otherwise run; and I agree that it would not be strictly necessary. In this special case however, it turns out not to be such a problem: The typical running time of one instance is about half an hour, the time spent in a critical region is usually a couple of seconds, sometimes half a minute, and the task to be performed is so that on a fragile Windows machine, I'm not so unhappy to know that with the present implementations, no two tasks are going to do the same in parallel, even though in theory they can't disturb each other.

Winders doesn't appear to let you unlink a file you have open.