Umbrella Insurance when you don't have a primary residence?

[Justin Levine]

Hello, 

I have a couple of rentals properties out of state and I currently rent an apartment in Los Angeles. 

Next year I'm going to get rid of my apartment, put all my stuff in storage, and live utilizing short term rentals a la airbnb and not have a "primary residence" 

I was looking at getting an umbrella policy and my insurance provider said I had to have a renters insurance policy if I don't have a homeowners insurance policy for my primary residence. 

He said he would have to write a new renters insurance policy every time I moved around..... I'm gonna be moving every month for the next year or two.... I won't have an apartment in my name. 

Is anyone familiar with an umbrella insurance option for someone that doesn't have a primary residence?  

Any help would be appreciated thanks!