However, my concern is how to effectively spend ~$750K via 1031 as a first time REI without A.) making an unwise investment because I'm rushed and relocating my family of six and B.)

The property has been well maintained, and there is a clear opportunity to add value by continuing a proven renovation strategy.

All that while state and IRS taxes on profits are increasingly challenging, as refinanced funds for construction in progress aren't deductible expenses, thus not lowering tax bills.All that said, the "snowball quickly" effect you mentioned isn't quite happening yet.

Although I haven't maintained a credit score stateside considering I left in 2010, I can qualify based on my finances where I live.

If your 401K is with your current employer, it is (effectively) impossible to make it an SDIRA. 

After doing this successfully 5–10 times, I’ve found it to be an incredibly effective strategy when approached carefully.I'm curious to hear from others who are pursuing similar strategies.

If we use an example of a $1 million gain, and assuming the seller is married and hence qualifies for the $500k exemption, then the effective rate is 1/2, so around 8.5% plus ossibly another 3.8% or 12.3% effective rate exclusive of the subjects decision to live in a high tax state. 

Finding a well-maintained home in an owner-occupied area with minimal rehab is a great strategy.

what will be the most cost effective tool to evaluate residential properties? 

This approach won't just provide you peace of mind but also maintain your independence as a landlord.