Don't worry about the 2x2 being strong enough. I bounced on it, and with my 250 lbs bouncing on it, there was no creaking or cracking. Don't forget that the 2x2 is also backed up by some plywood. If you glue and screw it together, you will have one integral piece that is much stronger then the additive strength of each component by itself. The area that you are spanning is very small. Try it, you'll see. Besides... if it breaks, you aren't 8' up in the air, only a couple of inches above the ground. It's not like you'll do serious damage to anything.
I used to help design and build theatre set pieces. You wouldn't believe how flimsy you can build a set piece and still have it take a load. A 1x4 piece of white pine every 24 inches spanning 48 inches will support a cast of 10 people with a 4 foot by 8 foot piece of 5/8 plywood screwed to the top of it. That's an average weight of 1800 pounds supported by 5 pieces of 1x4 48 inches long... I'm thinking your 2x2 will hold up to the test!
Mike
