If the current design/placement gives you good lighting, and you don't mind the look of the fixtures, then you can simply replace the flouro fixtures with LED T8 fixtures (available at Lowes and other places). There are also LED bar lights usually used for under cabinet lighting which have covers and are a bit more attractive (mine are Utilitech from Lowes), and strip/tape lights of various configurations. You will have to look at each type to see which will deliver the lumens that you need. You might also want to have some of the fixtures facing down, others up for the ceiling illumination, or use a combo of fixtures and tape/rope to achieve that. Maybe add a top to that open box to attach downward facing fixtures then place ceiling illumination on top.

If I were you, I would get in touch with inspiredLED.com or environmentalLED.com to discuss options; the first has frequesntly been very well reviewed on this forum and the second also just not as much.