What do you think is the outlook for real estate where your house is located? Is it in an up-and-coming area that is likely to appreciate in value and in rents, or is it stagnant or even going down? If it's stagnant or going down, get out NOW. Take the loss on the house (maybe in just a traditional sale), and you will recover from the loss in a relatively short time with your Mustachian ways.
But if the outlook is good, I could see some favorable conditions for renting the house and moving closer to work, saving on commuting costs and time, and gaining the tax advantages of being a landlord.
Even though you might end up with a somewhat small, negative cash flow renting, you stand to gain overall in the longer term if the house appreciates in value decently. For example, if the house gains a modest 5% per year, on average, then in 4 years your house will be worth around $182,000 (based on your estimated current value of $150,000). That $34,000 in appreciation will more than make up for any $200-400/month negative cash flow. And as previously discussed, you will likely get tax benefits for renting out the house plus savings in commuting costs.
There's some risk involved, of course, in betting on appreciation to overcome negative cash flow. But if you (or real estate pros) in your area see your neighborhood as favorable for appreciating in value in the coming years, then I would hold onto it, continue your plans to refinance, and rent it out to move closer to work if desired. Who knows, it could even end up being a terrific long term investment and money-maker for you as a rental!