There might be local banks or traditional options available, so I'll let the traditional LOs chime in.

I don't go to "closings" in the traditional, 'big table' sit-around-and-wait-for-suits, sense.

If you average permit filed price per square foot its about $135-$140 traditionally for the builders because they are adding basements.

That's when there's less than $50-75 in actual supplies (drywall, tape, mud, paint) needed for the job.I had an amateur suggest that he could do it for a few hundred.

Not sure what else unless a traditional bank would consider it

The structuring of a series LLC is much different from a traditional LLC and I would suggest you hire someone. 

Neither will a traditional bank. 

Tax benefits can help make a better business deal, but a bad business deal is hardly ever going to break even just because of tax benefits.The other big consideration you should have, in order to actually benefit from real estate fueled losses or credits, it will require a substantial investment of time - either to get over the material participation thresholds for short term rentals, or to get over the real estate professional thresholds for mid term /  traditional rentals. 

If you plan on doing 20% down, I would just recommend going with a traditional conventional loan...

And yes, based on what you stated we would need more information but let's take it at face value - what if you don't show enough income to get a "traditional" loan?