About 35 years ago, I flew into an embedded thunderstorm near San Angelo, TX. This was while receiving vectors from ATC to avoid. Wife said later that day we weren't going to do that again. Next week we ordered a Stormscope. Summer in the south and east coast, if you don't plan to weave around activity, you won't be doing much flying. What worked for me, learning over a period of time, was to avoid any area of convective activity as indicated by the Stormscope. Cumulus clouds that were 12000 feet tall or so, I would fly through. Taller they are, the bumpier. Wife's tolerance was less than mine. Other passengers, more so. I used that Stormscope for 23 years and staying away from convective activity, never got more than moderate turbulence. Look up the definition of light, moderate and severe. Many people overstate the level of turbulence. Light, the approach book stays on the seat. Moderate, the approach book levitates, then falls to the floor. Severe, the approach book leaps to the windshield, bounces off your head and hides in the baggage compartment. Severe, I had my car keys come out of my pants pocket. The OP said towering cumulus. To me that indicates a tall cloud my airplane can't climb over. 18000 Or more, if not a building thunderstorm will still have up and downdrafts and be more turbulent than you will try a second time.