What do you think about trying the deep water/bubbler system on a pot and tray system
Bubbling trays works fine for starting off, but once the roots really start to grow, there is no place for the root mass to go and expand into. The system you linked to is specifically designed for trees or plants that will eventually be transplanted out-doors or into large containers, so the roots are contained on purpose. If you are not going to transplant, you'll likely need different pots, unless you are doing a single-cola sea-of-green.