It'd be interesting to see a picture of you on your bike. I have essentially no "torso strength" but have never had any trouble taking my hands off the bars.
When I taught skills classes to introductory track riders, the most basic drills incorporated removing a hand from the bars. I never encountered anyone who had trouble with that part, so barely know what to suggest to you. I suspect you may have fallen for the modern nonsense of angling your saddle toward the handlebars, which will give anyone a hard time.