You really need to research the city you need to know every neighborhood understand the city good school districts and bad school districts top employers etc.

Can you qualify using employment history, tax returns and DTI?

None of your "solutions' pave a way for actually purchasing the property. 

PUSHBACKThis law unfairly targets small employers (>20 employees).

Economists note that job growth in typically underreported industries fell by 42,000 compared to the 6-month average, suggesting August’s numbers may understate actual gains.Key Employment GainsConstruction: +34,000 jobs, driven by heavy civil engineering and nonresidential trade contractors.Healthcare: +31,000 jobs, though slower than the past year's monthly average of 60,000.Social Assistance: +13,000 jobs, with more modest growth compared to previous months.Other growing sectors include financial activities, wholesale trade, and government (+24,000 jobs).Job Losses and Sector StrugglesManufacturing: -24,000 jobs.Retail: -11,100 jobs.Temporary help employment continues to shrink, reflecting business uncertainty.Wage and Fed Policy ImplicationsWages rose by 0.4% in August, up 3.8% year-over-year, supporting a cautious approach by the Federal Reserve on deeper rate cuts.

Do you have any idea how many people these entities employ?

Also be aware of Unrelated Business Income Tax (or UBIT) on leveraged real estate inside of an IRA.Or better yet, since you are self-employed - go with a truly self-directed Solo 401k plan, which would be a much better option and will help you avoid the UBIT on this investment. 

If you are self employed you can also look at bank statement loans assuming you have a business with high deposits.

is there a particular formula that takes all manner of factors, (employment growth, corporation development news, barrier to entry, rental rates, wage growth, etc) into account and spits out an "invest in city X" answer?

Im self employed and my debt to income doesn't look good on paper.