Just had a thought, thinking about something I did recently... I didnt care much for params since I had my own components doing the heavy lifting.. So I used the $state provider and pulled in the url, split by / then use what was on the end. Why dont you do the same with the ? and the &? Then split each result by = for your key value pairs and run as needed. Just one of those shower thoughts haha.
EDIT: Nope sorry, completely ballsed that one up. If you want your params, add to the menu item:
Do not add = in your menu link. Just do that and your stateparams will be available.
ie: your menu link will be.
Your $state.params will be