I debated whether or not to post this because I am speaking from a Canadian context and that may not useful to you. In other words, I don't know what opportunities have typically existed or currently exist in the US scene so everything I write below may be useless to you.
That said, the kind of work you describe is quite prominent in Canada. There are a number of small-cap companies listed on the Toronto Stock Exchange that do this sort of work, and they target a number of commodities such as gold, nickel, copper, uranium, REE, and diamond. They typically work on projects upstream of any mine development/production and that means they are very volatile. Due to this, many Canadian geos form their own consulting company and work as contractors. It's a good gig when the investment market is favourable, but we've been in a two year slump and its not clear when that will end. Many geos are out of work; myself, I have left the industry entirely.
Now, on to some of your questions:
I want to ask the rockhounds of Reddit, what would make me stand out for an entry-level exploration job with firms that work in remote and desolate areas with the most unfavorable conditions.
Ex-military guys stand out, so push that narrative. Experience in exploration methods such as mapping, drilling and sampling are also crucial. Claim staking, prospecting, GIS, statistics, compilation reports are also good skills to have to flesh out your profile. Unfortunately, many of these require jobs already. Smart students in Canada get a prospecting license and practice these skills on their own claims. Shows initiative and the will to make shit happen.
Companies that possibly include Geophysical surveying for economic deposits. How would I even search for these companies?
Go to the TSX and get a listing. Many are Canadian companies that work in the US, others are US companies that list in the TSX to tap into the relevant investment market. It will take some time to wade through, but it will start giving you some perspective on how that part of the industry operates. If you find an American company that seems interesting, head over to sedar.com and find a technical report (NI 43-101) to see the kind of work that they do in pure technical form. This won't necessarily improve your chances of getting hired, but it will give you perspective and perhaps allow you to stand out in any interviews you might get.
Does anyone know what the turn-over rate for these positions are? Are they more susceptible to global economic trends compared to other specialties in the Geology field?
Working at a mine site in exploration can be fairly stable, but expect a lot of instability anywhere else. Junior companies are very poorly managed, and their choice of investment model is at odd with the lifecycle of their projects. I have seen no effort to even really recognize this, to say nothing of mitigating or fixing it.
To combat this instability, your best bet is to get the widest experience possible in a range of deposit types/age and exploration methods, and if you feel like you have the chance to lock something down for the long term, do so. Also, really learn how to market yourself and network. You don't learn this in school, and contrary to all the emotional turmoil students expend on topics in structure and geochemistry, this will be your biggest challenge. And I don't mean sign up for an event and wander around. Really learn how to wheel and deal and bullshit. I can't do this, hence why I am done. Most of your leads will come from people you know, not seducing HR departments.
Has anyone here ever worked in this type of field? What makes a candidate stand out if you were to hire someone to replace you or your underlings.
Working in exploration is tough, and new entrants typically don't realize this. They have romantic visions of hiking through picturesque scenes reminiscent of Yosemite and fail to realize that much of your time will be spent slogging through dense bush or swamps, getting eating alive by insects, or getting pissed on by every cloud that wanders overhead. It's not fun work. Sometimes, like on a soil or humus line, you don't even look at rocks.
I can't trust people like this. They're the ones heading back to camp early, or wanting an office day because their $300 goretex boots crapped out and are now wet. In my experience, military guys get this. I had the pleasure to work with some ex-Canadian Armed Forces personnel, and after the first day, one of the guys says with a big grin on his face, "it's just like Afghanistan except we're not getting shot at." They were excellent workers and I'd fucking hire them back in a heartbeat if I could.