So my plan is to avoid burning out and I don't care for putting on the golden handcuffs of a mortgage, luxury car, etc. I'll have no student debt. So, I figure if I can make 100k/year (before taxes) I'll be living my dream life. How many shifts per month will accomplish this is it pretty easy to find such a gig?
This is the Chupacabra or Big Foot of Emergency Medicine. It exists in theory but just doesn't seem to materialize. Others above have pointed to why, but mainly it comes down to overhead. Every doctor in every specialty has a fixed amount of overhead expenses just to break even for yourself or your employer. It may be less for EM, but still exists. These are fixed costs that aren't less because you work less, they are fixed. Even if you work zero hours, you (or somebody has got to pay them): malpractice insurance, health insurance, DEA license, society memberships, retirement fund, administrative fees, etc.
In other words, it costs money to put you out on the floor. So the amount you are generating per hour is negative dollars per your day 1. Then at some point you see enough patients to reach $0 per hour, then as you keep producing, the hourly climbs steeply. Then it climbs even higher and more than linearly as you get above the clouds (the clouds being your fixed overhead you're done paying).
Just think about it. Is there really any reason a Dermatologist can't work 2 days per week?
Why not for a Neurosurgeon? They generate a hell of a lot more money than an EP. Why can't they just find a hospital that signs up 3 neurosurgeons to "job share" hours?
It comes down to money.
It's cheaper to have one guy who want to work hard (1/3 the malpractice policies to pay for, 1/3 the licenses, fees, recruiting, and so on and so on).
So in theory, your flying unicorn job may be real, but you just ain't going to find it. Why?
Because a work horse is just a whole lot more practical, less high-maintenance, and a hell of a lot cheaper.
Trust me dude, if this flying unicorn existed for all of us, don't you think we'd all be riding it?
Oh you're right, this exists, but once you show up it's, "Oops. Sorry, we're a little short staffed. Would you mind working a little extra?
Just for a little while?"
For every, 6 shift per month unicorn, I'll show you 10 work horses working 3 shifts per month more than they want to.
My suggestion: find something you like enough to work 40 hr per week at.