Hey! Not a doctor, but maybe it has to do with acid reflux? The acid can irritate while you're lying down and cause the hiccups.
Maybe for a few nights try elevating your head a bit and taking a Tums before bed. It's probably the least harsh over the counter med I can think of. And during that time, avoid eating a lot of fried or acid foods (tomato sauce can be killer!). Garlic and onions can also agitate mine.
Also, if you don't already, I'd cut out carbonated beverages, even sparkling water.
If that seems to help, you might want to talk to your doctor about more permanent solutions.