Just wondering if that is the only way to sell a property and not have to pay any depreciation recapture.

They pay the rent on time, every time, don't damage the house and don't cause any problems.

Insurance would cover it, I would pay the deductible, and no assets would be lost.If you are in an area like San Diego where people are more likely to sue, a judge is more likely to find you guilty, and the payout is expected to be higher, you may consider an umbrella insurance policy.

None of us own the home, we just pay the rental company.

If a put a down payment on a home and begin renting it out, is it okay if the property just pays for itself and I don't make any positive cashflow?

While you are at it, learn how to manage your properties well because a large percentage of investors lose tons of money through rookie mistakes with non-paying tenants, unscrupulous contractors, long vacancies, etc. 

I'm not sure there are many syndications executing investments with debt funds today and paying 10% of the property's value to buydown the interest rate and claim positive financial leverage. 

It may be a frustrating few years until the area grows around you, but can pay off in the long run.

I’m thinking about selling one of my debt free rentals to pay off the loan of the new house – thus erasing the $3500/month loan payment.

Or will you send a licensed electrician and pay $100 to reset a breaker?