However, they perform all of the concierge services including advertising and booking.

Then, how well you execute your strategy.Most people consider all costs prior to the rental being "placed in service" to be "start-up" costs that will factor into your COCROI.

Recourse or non-recourse? 

I have been talking to customer service for 2 weeks now because the software will not link to my bank account. 

Even if you create a non-CA LLC, if you are managing the business from California, you will likely be deemed to be "doing business" in California and therefore likely subject to CA taxes.

Likewise if you have any advice on this strategy (for example - things to be aware of when working with a full service turnkey company like this?) 

I don't think I can go back and claim those when we moved the property into the LLC and actually put the unit into service.

I know I looked at Cozy and a couple of others at the time I was deciding which service to use, but honestly I can't recall the comparison specifics. 

Another thing you can do is set up an LLC with a third party service as agent, and that same or another service as manager/member.  

And while ultimately I'd like to have a multi unit of my own that I actually house hack, for now I get to live in a first class building (maintenance free) on a non-first class budget.