My circumstances don't allow for up front payment but I would be willing to pay with profits from the the first few deals.

In Texas (and most other states that have the series LLC structure), no series is liable for the debts and liabilities of another series (except in certain statutorily defined circumstances).

There are special circumstances and nuances to that in every state, but for the most part that is how it works.

If the interest rate is lower than current rates, they would be less inclined, if it were higher then their motivation may be greater.Here mortgage terms are shorter (typically 5-years), so there is little chance the lender would order a new appraisal unless there compelling circumstances (i.e. the Vendor had completed a major upgrade to the property since the mortgage was subscribed).  

If it were me I'd concur with @Fred Heller's perspective on holding the property despite the overall carrying costs (provided it's not a significant financial burden and holding makes sense for my personal life circumstance, e.g. hassle benefit ratio).

Perspective tenants don't want to live next to a sex offender or a violent criminal regardless of the circumstances.

Each property is different, the circumstance of sellers and buyers will always be different, that takes your flow chart to unlimited variables, many functions are the same, but you'll have different choices and paths to reach your desired results.

Correspondingly, all business income taken from an LLC under similar circumstances is subject to self-employment taxes.

Sometimes a seller has a circumstance that compels them to leave. 

In some circumstances those unknown conditions of the property, which require substantial repair and translates into larger capital demands, can become a fast track to zero profit and losses.