I need to replace my double pane windows due to failed seals, so I recently googled options for reducing noise too. Turns out there is very little difference between single and double paned windows for noise reduction, and the best way to reduce noise is to install a second set of windows. Something like this
Window Noise Reduction Comparison
I like the curtain idea though, so I'm going to try this first. I'm surprised you would be willing to purchase something that you can't keep. Curtains would probably be your best bet since you can take them with you when you leave.