Get Chart 11369, it's about 23 miles from Bayou Bonfouca to the Tchefuncte River entrance. You'll see the north draw is 42 feet when closed, while the south high-rise, though much farther away, is 55 under the fixed span.
STAY WELL CLEAR of Goose Point, it's way shallow out to almost a mile off. Otherwise, should be an easy reach in the typical summer southerly. Check with any sailors you know from Madisonville about the depth at the channel bar, years ago I got in and out fine with 5' draft. Maybe check with the St Tammany Sheriff's dept, their patrol boat folks should know. Also they're the ones to call (other than Sea Tow) if you have a problem, since they're local.
Also, the lake height varies with the wind, with strong easterlies making it higher by a foot or two, southerlies to but less so, and northerlies and westerlies (less frequent in summer) make it lower. This may help you if the bar is shallow. Don't be shy about heeling your boat way over if you touch, it's just mud and usually this will get you free.
Good luck! Madisonville is a pretty little town, and you can wander pretty far upriver, it's a scenic ride. Ask the locals first about draft/depths.