@Vanadium 50 ,with respect to the first job post that the OP linked to, you are flat out wrong that the job requires a PhD -- the scientific software engineer position specifically states that their required requirements are for a "Bachelor's degree in Astronomy, Computer Science, Physics, Mathematics, or other relevant engineering or science field." So the OP would have the bare minimum qualifications degree-wise with respect to that position.I am not sure you are listening to me. Even when the jobs do not say require a PhD, that is what they are looking for. That's the level of experience they want, even if they do not use that language. That's certainly who your competition is. That's who they are hiring. In my estimation (I am not an astronomer, but my department has several and I am an APS DAP member who has reviewed telescope proposals) none of these jobs would open up had you had a BS in physics rather than applied math. None.
Another position that the OP linked to involved an Instrumentation Specialist position, which specifically stated that the applicant must have a "Bachelor's degree in Engineering, Physics, and related field" in addition to previous job experience. None of these positions are the kinds that would either require a PhD, nor would employers be looking for PhD holders specifically.
Granted, I'm not certain that a physics degree on its own would make the OP more competitive in these positions either -- if anything, a degree in electrical engineering may be more useful instead.