New to this forum, but maybe I can help - so let's get to the nut of your problem.
As I understand, you can go work for your lender to the tune of 160k per year per three years. You said 120k, but we need to add in the 40k per year loan forgiveness for those first three years to the value of your compensation.
You can also go work somewhere else for 160k a year (yes I know you said that's the starting range, but there ain't no guarantees in life & who knows what your negotiation skills are, so let's stick with the base figure).
So where we're at is that your job will start at a market rate of 160k regardless of where you go, which should make your decision easier.
Let's address the other facts first, since no item stands alone - everything must weave into a tight badass web if you're truly on the path to FI.
Start with the savings (20k). Under no circumstances do you start paying down this debt with the small amount of change that you clearly need, as it's less than four months of your current living expenses and you apparently have no other (non-usury) means of financing.
Second - the wife. She needs to be on the same page with you RE:FI. If she's not, then fuggetaboudit. Where are her earnings? What does she do? What's yours is hers & vice-versa, so it's hard to give advice without the involvement of the other half.
Third. The underwater house. Do the math. How long do you want to keep it? Is there any emotional attachment on the part of the wife? Hint - there can't be. It's now an investment. Will it make you money? ROI? Need more input on this too....moving on.
Fourth. Your current situation. Seriously 70k to live in Cali? Fix that asap. Since you're renting, shouldn't be hard to find cheaper housing. I've lived in two of the world's most expensive cities and never made more than 50k a year. Don't say it can't be done. Those people that cut your lawns, serve you food, clean your house, & do all those other service jobs? They live somewhere near by, not all of them commute one hour and not all of them live in the ghetto. Find out where they live and emulate their lifestyles. I lived in some seriously dodgy neighborhoods & never had a problem. No one thinks twice about someone that looks and acts like they belong in the neighborhood. I drive the same pos vehicles, wear the same second-hand clothes & drink the same cheap beer. No one knows what I have in my bank account. Hell, read the Millionaire Next Door. Some of my much older more frugal neighbors (plumbers, electricians, roofers) probably have a lot more of a stash than I do (I've looked up their homes, no mortgages). Okay, I'm rambling...point is, TRY HARDER to cut the living expenses to below 30-40k.
Back to the loan situation. I think logically, so let's assume first that you cannot find a way to come up with the loan money. This one's easy - you work off your debt. So you're at 160k and you have to move (since you stated the place where you have to work off your loan is somewhere else). Not so much of a bad thing, since you get a chance to reset (and we don't know the cost of living of your new area, so that should be a factor too). Wife not liking it? Not so much a factor unless she is a major earner herself, otherwise, for better or worse, richer or poorer, etc....she needs to deal with the new location as it seems the default most-likely option. One of my best buds spent three years of his life in Iraq & Afghanistan. Did he want to go to those places? Of course not. Sometimes we make choices that have consequences, and as they go yours aren't so bad.
Option two, you find the money & go where you want. At 160k a year it's a wash. You still need to set up shop & get those expenses below 40k a year. Let's assume you do - and also that 60k of your income goes to taxes. You're still stashin' 60k & 60% of your income. Not bad for a starting point. Then you work, your salary goes up, expenses go down and you're up into the 70's and and you're golden in less than 10 years.
Where to get the money - you're looking for an unsecured loan...well it's secured by your future earnings. You could get a life-insurance policy and try to convince a bank or investor to give you a loan. If I had the cash you needed I probably would in exchange for a good interest rate (think 25%+) and being named as the beneficiary on your life insurance. I also know people that could do the same thing, but trust me you don't want to default on their loans. In any case, such a loan is high-risk. Other things could happen to you hypothetically that result in you not earning but remaining alive...don't want to go down that path, because it's dark. I don't know any legitimate places that are going to give loans of that size without collateral. The only thing in the US similar is student loans, but that's a different animal altogether because of their non-dischargeability in bankruptcy (as in never being able to shake them as long as you live).
Seems like your only options are getting someone to put up some serious collateral or stick with the debt-workoff job. Then picking where you want to live, and paying down that loan yesterday while working hard to put some serious MMM principles in action.
Thoughts?