I don’t see how this will help avoid providing t_f as required by the library… You can augment you state with time if you wish the way you described (and as described in the book). But then you still have to provide some terminal time t_f. This sort of augmentation will not change the time scale.
What I did above is scaled differential equation by factor of time to make sure terminal time is 1. So at least we can provide terminal time now. But we can’t provide initial value for augmented state then as it equals to terminal time now and should become a decision variable.