Remote Hiring for Consulting?

I am looking for information on recruiting for experienced hires. I'm maxing out my salary band at my F500 company and am looking for alternatives once I graduate with my doctorate. I live in the Midwest but not in a major city (capital of a state, Kansas, Oklahoma, Arkansas, Missouri) for consulting. Is there any chance for me to recruit to a major consulting firm? T2 would be fine. I make ~135k base salary but bonus is only up to 4% of salary, so I don't even count it to be honest. Don't love my current job but like being near family on weekends. High performer at both companies.

Age: 30, male

Education:

• Big State School BS/MS in Systems Engineering (2014, 2016)
• George Washington University Doctorate of Engineering (spring 2022 most likely)

Work Experience:

• Software Engineer Intern at F500 (May 2013 - May 2014)
• Software Engineer 1 (May 2014 - Dec. 2014) -> took return offer but didn't like boss; internal transfer
• Test Engineer 2 (Dec. 2014 - Jun. 2016) -> worked FT during masters degree
• Corporate Engineering LDP at different F500 (Jun. 2016 - Jun 2018)
• Senior Engineer 1 (Jun. 2018 - Oct. 2019) -> stayed after LDP
• Engineer 4 (Oct. 2019 - Present) -> Returned to first F500 

Questions:

• Can I leverage my (new) degree / can I recruit for Consulting?
• Do firms hire in non-large cities, or would I need to move to Kansas City, Dallas, Chicago areas?
  • Would prefer to stay where I am but understand if firms are centralizing their workforce
• If not consulting, should I try to get into Tech remotely?