Is it feasible to become a paramedic full time and do a PhD in an unrelated field? Do you think this is reasonable? 
I am graduating with a BSc in neuroscience next year. I would like to be a paramedic for a little while (throughout my 20's) before switching careers and becoming a researcher in Neuroscience (for my 30's +). 

Scenario A:
After completing my BSc I want to do the 2 years of training to become an EMT. A full time work schedule as an EMT would be something like 12 hour shifts, 3 days on, 3 days off, 4 nights on, 4 nights off, etc. Would it be possible to pursue a masters and a PhD in Neuroscience while working a schedule like that? I imagine that this way I would graduate towards the end of my 20's or early thirties with a PhD. Then I would like to begin a career as a researcher/lecturer. Does this sound impossibly difficult? 

Scenario B:
After graduating, spend the next 2 years to become an EMT. Work as an EMT for a few years, then reduce to part-time or quit and pursue funding for a masters + PhD in my mid 20's. I hear that returning to university after a few years off might be more difficult, both to apply, and to be competitive. Is this true?

Scenario C:
Pursue my masters after I finish my BSc. Then do the 2 years to become an EMT, work as an EMT for a few years, then do a PhD. Will the relevance of the masters depreciate over time? If I already have a master's done, how long would it take to finish a PhD? 

I guess in general, is this just an insane plan? Or is it possible?
A does sound impossibly difficult to me.  The first few years of a masters/PhD sequence are usually based on coursework.  You will need to attend classes regularly on weekdays, which seems like it would probably be incompatible with a paramedic's work schedule.  Even beyond coursework, particularly in lab sciences, you may find that parts of your research have to be done on a particular schedule.

Moreover, at all stages of graduate study, you should expect that your coursework and/or research will require a time commitment at least comparable to a full time job (40 hours per week), likely substantially more.  Many graduate students struggle with the workload, even without added commitments.  Adding a full time job, especially one with as much stress, long hours, and sleep disruption as a paramedic must have, seems to me like a burden well beyond what any human could be expected to successfully bear.