The pipes work a treat. Just make sure that you don't go much below 100 mm in diameter, otherwise the contents get clogged easily and you have to remove the whole pipe to remove the castings when it is time. Less then that is difficult to get youtr hand in and out of too!
Ants can be a bugger, indeed. As you say, its best not to allow them access in the first place but they are tenacious critters and will find a way in when they want. It's interesting that they went for the bottom tray rather than the top. That suggests to me that they'r elooking for a nesting site, not just foraging for food.
RE: Worm havens