I am sorry that I am too lazy to read this thoroughly, but to me the original problem seems a mere illusion and a strawman. A priori, the two experiments are different, but who cares? The experiment with its stopping condition yields a distribution of results only if you have some assumed a priori distribution over the patient population. If you change the stopping condition without changing this distribution, you change the experiment and you get a different distribution for the result. This has nothing to do with evidential impact. Frequentists don’t, as far as I can tell, claim anything like that.