I've stumbled across similar wifi systems before. IF you're lucky, sometimes the bar on top will show again to let you change tiers or log out.
The quickest way I can think of, is calling front desk and have them reset (or even to cancel your acc), to force the login screen again. Or else try the router page (might be 192.168.0.1) to see if the splash appears again.
Regarding the lounge, it's at the discretion of property. It's not a big deal if the lounge is quiet. I would ask the lounge staff instead of front desk regarding that though.
Sorry, read your post again and you've already done all that. Just change rooms. If you really don't want to move. Ask for a check-out and check-in to the same room. Should fix it.
Good luck!