This is my first purchase (don't want to do anything stupid) and the rents could swing 600/month depending on what I'm allowed to do in the basement - I'd be in the red from a cashflow perspective if I can't duplex them.Am I rolling the dice here / do you not typically find out for sure until you close and begin renovations?  

You can roll the cost of refi into the refinance itself which will limit what cash you pull out. 

What advice would you give me to get rolling in the next few months?

In a box, $7,200 rent roll on $600k is very good, but we have to be missing some stuff here.

And some of us been replying back yes there is, just where they are, how to get them, has changed a bit and it's no longer as simple as closing your eyes and randomly throwing darts at a MLS map and buying whatever. yes, those days are long gone but if your willing to roll-up the sleeves and get professional at it, there is "deals" all over the place, you just gotta get skilled on how to find them, tap them, monetize them. 

Another approach could be to use LPMI, which rolls PMI into a slightly higher interest rate, potentially saving you monthly PMI payments.

Basically you sell one investment and roll the money directly into the next investment.

I've been anon lurking for years but am quite keen to roll up my sleeves to learn more.

If you have a rent roll that is great. 

This is Cleveland, everyone is buying for rent roll of 10% ++ net per year.