I would perform a test during due diligence to see if it is working properly, and if it isn't calculate the cost to repair and demand as a credit at closing.Make sure you build in the cost of pumping.  

( maybe it's better to wait out the low demand a little and stay at the current rent to not get a vacancy )The goal here is to increase cashflow and not to fill all the units ( if you can choose between to have 3 renters with lower rents or 2 renters with 1 vacancy it's better to have lower rent and 3 renters)If you still aren't satisfied with the situation, you can try and raise the rent in one of the month-to-month units to try the market, if the rent works and u get a renter=good, continue with the other 2, if not, switch back to the old rent to fill your unit again.About the month-to-month leases, i would personally try to switch them to 6-12 month leases with different expire periods ( 1 in april, 1 in august and 1 in december/spread out over the year so you get more flexibility with higher/lower rents when the leases are up to maximize your cashflow) this type of thinking works better the more units you have. 

We're trying to lease a high-end unit that will demand a rent premium. 

My advice to you is to find a run down duplex, put your 3.5% down payment in and use your other cash to fix your duplex up to a standard that would attract nicer tenants and demand a better rent per month.

Bloomberg wrote about Sam Zell, famous value investor, in a May, 2010 article, “Zell’s Firm Raising $500 Million for Brazil Propertyâ€: “Billionaire investor Sam Zell’s Equity International is seeking to raise about $500 million to step up investment in Brazilian real estate, betting interest rate increases will fail to stem demand as the economy grows at the fastest pace in two decades.

I figure doing the cash out is higher risk, so it would demand a higher rate.I then decided to check out my local credit union and they are telling me that the rate doesn't changed to much, regardless of a refi or cash out refi. 

I am not as in demand as @Jay Hinrichs, but the truth is I am probably just looking forward to talking to someone who shares the same interest in real estate and is not someone wanting free legal advice or someone I put in jail.

The answer is 'Sorry, that is not available due to high demand.'As

Demand a setting that will provide you with intellectual capabilities that allow you to expand your mind instead of directing it.

The good ones will demand a contract because they want to hold YOU accountable...good contractors would be appalled that you didn't want to sign a contract.I think you need to change you thinking on what a "good" contractor is...