Well heck, for $300 you should be able to find something...I had a ferret cage that was the size of a refrigerator and had multiple levels, and it was only about $100. It would almost work for you as is, instead of using ramps between levels you make the shelves overlap each other so they can just jump from level to level and can't fall all the way down, some of them have additional snap in shelves that you can purchase.
The down side is that if the rabbits pee on the shelves they will manage to hit your floor, and cleaning the shelves is sometimes a pain, depending on the configuration. Ferrets are all box trained. Anyway, look at these.
http://www.ferret.com/cages/cages/887/? ... QgodUCQ6iw
You could also move the x-pen indoors on a hard floor (kitchen maybe) and work on litter box training them, so they could have some out time...after they are box trained you could let them run around in the house occasionally, when the 3 y.o. is napping and the dog is confined in another room. You would have to rabbit proof (cords and other chew-able things) and you would need to supervise...
Even just a wooden board for a shelf can give them more space if your cage is tall enough to allow it.
Also, I am not familiar with spayed/neutered rabbits. As they mature, it is possible they won't still all get along isn't it? Or does altering them completely rule out that possibility? That is why Ottersatin is suggesting 3 separate cages--our intact rabbits would possibly decide to try to kill each other one day.