You have to do what works. I've yet to find a lake where I couldn't catch brim with a 1/64th oz. jig with or without a float, but I haven't fished your lake. It may be that the forage in that lake is all in and very close to the weeds on the bottom and that is the only place the fish are looking for food.

I have had days where live bait worked much better, but never get skunked using a very small jig. A lot of the lakes around here have the same green slime and the key is to get your retrieve speed to keep the jig a foot or so above the weeds, or to set your float so the jig is no more than a couple feet from the bottom. Jigs under a bobber are usually only real effective for me on the flats where the depth doesn't change much, and the retrieve speed almost always needs to be painfully slow. Then it's just a matter of finding the right depth to set the bobber. If your lake doesn't have flats that hold fish, the only other good way would be casting parallel to shore so that the jig will be in the range above the bottom that the fish are looking for much of the retrieve. In any event, you know where the fish are when you're catching them on the drop shot and you need to be able to get the jig into that same area. It can be difficult to do without fouling the jig in the slime unless the fish are very aggressive that day. Like deathb4disco says above, you have to commit to fishing the jigs in order to get a feel for what works. When I go fishing by myself and am not trying to put family members with lesser fishing experience on fish I don't bring any live bait. Sometimes that leads to pretty slow days, but I also often have days where I know I catch even more than I would have with waiting for the fish to find the live bait. Also keep in mind that unless you are able to get very close to the fish, you really need to fish 2 lb. test diameter line in order to fish a 1/64th oz. jig without a bobber.