I don't think a goodie bag is that big a deal. The party is the goodie bag. You don't need to send a gift home with your guests. One cheap thing to do if you really feel you must is to get a bunch of helium balloons. Send each guest home with a helium balloon. The kids love them and they are cheap if you buy a bunch at once. You can decorate them and then send them home with the kids. Just a thought.
As for the opening of the gifts, I think it is rude to not open them and thank each child before they leave. Especially little kids...the giving of the gift is one of the most important things. You see them crowd around the birthday kid? It is because they want affirmation that their gift is appreciated. They are saying, "Open mine! Like mine! See mine!" It is important and when you don't have that, kids are disappointed.
A few thoughts: We rented a place that didn't give us time to open the gifts or allowed us to pay an extra $100 for a room to open them in. Out of our budget. We went to a sonic playground nearby and opened them. We had their cake there too. The parents ordered some drinks and we didn't stay long and Sonic didn't seem to mind. I had a friend who did the same, had her cake at the sonic nearby the jumphouse place she rented, and she asked them for some half off coupons for drinks and they gave them to her. Then she bought everyone a drink (half off) and she chose the size. They just chose the type.
If there is a park or playground nearby, you could move there for the gift giving. Parents usually don't mind moving to spot B if they know the reason why...we've all had to rent those places that don't give you a lot of time without a big expense so I think everyone understands. Anyway,that is how I would handle it.
Good luck.
VickiS