Replace the fluorescent tubes with 120v 4000K LED tubes. We replaced our 3 fluorescent bulbs in the laundry room fixture with LED tubes and have good light output. Or, replace the existing fixture with an integrated LED fixture (similar size/shape to the existing fluorescent fixture).

We replaced ours with two round 4" flush mount LED and have plenty of light.

It would probably be pretty easy to replace the existing fixture with a circular or rectangular LED panel light which you might be able to attach to the existing ceiling electrical box (check how the current light is attached and wired before buying anything). Some models offer selectable color temperature; you could choose a warmer color to make the room appear less sterile than it does with the fluorescent. I'd get a dimmable one. Not really stylish, though.