Try using a slightly heavier jighead to reach the bottom. Going light as possible is the way to go... but the key in that phrase for you seems to be the 'as possible' bit. Current, water depth, the type and size of your SP tail and wind will all play a factor and I'm constantly changing up the tail to jig head combinations to suit the conditions on any given day.
I range between 1/8 oz (rarely, but sometimes a little heavier) and 1/20 oz for flathead. 1/8 oz for when there is quite a lot of wind, a strong current, a bigger SP tail on the jig and/or I need casting distance. Will always prefer the lighter jig heads so long as I can get to the bottom and the tail works in the water properly (eg you can't tie on a gulp 4" grup and expect the tail to work with a 1/40oz jig head). While you're figuring it out, drop your rigged SP beside you in the water and make sure it's fluttering before you start casting. If not, you've either not rigged it right or, more likely, it's not got a heavy enough jig head on it.
Most people cast into the direction of the current flow so that the movement of your SP back to your rod follows the direction of the current. This is more similar to the energy efficient activities of fish. Also, species like flathead and flounder tend to face into the current when waiting in ambush (water flows over their gills better and also the way their prey tends to move) so, if your lure is coming toward them rather than from behind, there's more time that they get to see it and decide to bite.
Also, you shouldn't be casting against the wind. Position your boat well (or choose your landbased positions based on tide and wind before you head out) so that you can cast to the target structure with the benefit of the wind behind you. Bonus - then you can go lighter with your jig heads.