Any guidance or ideas on what could be the best route to take that would be somewhat economically feasible, can be established relatively quick and has low overhead to run and operate would be greatly appreciated. 

Another vote for the midwest, I will chime in for the Indianapolis Market - huge economic diversity, low unemployment, low cost of living, low property taxes, landlord friendly, big investor community. 

Remember too, the interest rates are a commodity item and are dependent on current economic climates.

The roughly $110 million plant, which is expected to employ about 580 workers at build-out, represents a major economic score for the Hill Country city, considering the public incentive package offered to land the project included a $3.3 million land acquisition grant and $1.8 million in infrastructure improvements.https://www.bizjournals.com/au...

I'm trying to educate myself on the process (if I decide that the economics make sense) of scraping my house and building a 12-unit apartment building. 

First step is to look up the property on the Zoning map to see what you can build by right and that you have the appropriate property line setbacks.If so, then it can be a good next step to familiarize yourself with the building inspectors and the process.If not, then it's best to go to an experienced Zoning attorney and discuss whether it's possible and economically feasible to try to build a 3 family on the site.

The remaining economic life for the home is only 15 years and the term requested was 30.

Unfortunately in the current economic climate some landlords will have to sell their properties.

Depending on the penalty, if at all, will impact the economics of your refinance. 

One of my daughters economic mentors a few years ago,  explained how they converted their old garage, detached, to a unit for STRs.