If the fluorescent bulbs are working, I'd say just sell it as-is. The LED conversion would add value, but unless you've got a bunch of extra time, I don't think it ends up being a lot more money.
Pool players are a suspicious bunch. No matter what they do, someone will think it's rigged. On the other hand, no matter what they do, someone will try to rig it...
If you're looking to get something new altogether, there's a guy here who sells LED perimeter lights in a few threads. I bought one a couple of years ago and it's been great. It was exactly what I wanted and was reasonably priced. Great color, no glare, and it really looks great in my room...
There's room in the world for both chunky AND creamy peanut butter. Variety is the spice of life and every table doesn't need to be the same. As long as both players are playing on the same table by the same rules, the game is fair. If some players favor certain conditions, all the better...
This sounds so very familiar. I went through this with my father, exactly as you described. You did the right thing, and he's lucky to have you in his life to look out for him. Hang in there.