Sell, HELOC or Cashout Refi

[Sheldon Yoder]

We currently own our primary residence and rent out the basement apartment. We are getting $800 a month for the basement, but I believe we can get $900 when this tenant moves out. 

We are looking for a new primary residence, and that is where my question is. I would like to be able to keep our current property and rent out the upstairs as well, making it a nonconventional duplex. I think we could get $1,200 for the upstairs. Our mortgage on the property is $1,275 a month, so we would cash flow roughly $800-900 not counting repairs. 

We have approximately $100k in equity in the home and I need to access about $35-40k of that in order to purchase a new home. Am I better off to sell our current home, get the full $100k out, and then try to find another rental? Or, should I try to do a cashout refi in order to access some of that equity to purchase a new primary. The loan would be more long term so I don't love a HELOC. I talked to several local banks and they could do a cashout refi, but my interest rate would go up 0.5%. Worth it? Thanks!