Thanks for the replies everyone. The squeaknomore screws look like a good idea, I just may try them out. I have noticed there are areas where it squeaks less, though usually they are near objects that would make it difficult to jump rope in, like the bathroom or kitchen. I think I might be able to though if I move one of my couches. If squeaking weren't an issue, and it was just the impact noise that disturbs the neighbours downstairs, do you think just using the incoming mat will help?
These are good ideas. The laundry room is huge and has a slate flooring in the basement, that would work perfectly for my needs. I'd just need to get over the odd stares I'd get for working out in the laundry room as people come down to use it.
As for asking my neighbour if there is a good time of day to exercise, I've tried that but she thinks im trying to find out so I can break into her apartment when she's not there. It's sort of a bad area of town, but it's cheap cheap to live here so I can't complain.
Thanks for the advice, it has been very helpful.