Because I know now that there is no genuine interrupt caused by the
timer device based SOFTINT, what possibilities do we have in order to
cause such interrupt requests? That's because I really need constant
periods and I would speculate that task based code executed is more
often interrupted than a genuine low-level interrupt code (?).

For regular periods you can use WAITCPUCLOCK unit of the timer.device. Then you will ensure your requests will return in regular periods of time and latency between receiving the returned request and sending a new one is irrelevant. Of course it does not protect you against a case where your process is scheduled out by exec...