I work for a third party auction company in Texas and though a month or two may not seem like it isn't enough time, it actually is if you have your buyer list available. 

A real estate attorney can assist with drafting a partnership agreement that outlines the rights and responsibilities of each party and addresses any potential contingencies.

FCI covers almost every state, are not overly expensive, but they are a big company and sometimes the different parties don't communicate well with each other.I have also used Allied and August servicing with good results.

Sell the entirety to yourself (through an unrelated party) and do a 1031 on that sale. 

I recommend having a local experienced investor (an unbiased party not someone trying to sell you something) do a detailed video tour of the property and the street/neighborhood before you submit an offer and paying them for their time $100 or $150.

The third-party appraisal came in at $110,000 so regardless of if you "know" the property is "worth 120-140ish" , we can not lend based on your opinion and must utilize an independent-third party value. 

Do people hire a second contractor or an entity to assist as a neutral third party to determine things are complete?

Since there is no custodian involved, you must be scrupulous with your investments and have a good understanding of the rules against prohibited parties and prohibited investments.

In every transaction the buyer would be getting money to put for a down payment and then funds from a third party are the balance of the loan.

What party of Houston are you looking for a property manager?