I worked for 3.5 years in an unrelated industry and have just been accepted into multiple PhD programs without a masters. I shied away from a Masters program because, rightly or wrongly, I've perceived them as a way to quickly boost your salary in industry, segue into a new field, or bolster a poor undergrad performance (Or just prolong your life in academia...). I personally decided I didn't want to pay for my graduate education, and because my undergrad was solid and in my desired field of study, it did not seem to be a profitable decision for me.
I, too, am very debt-averse. Is the debt you will incur from this master's and potentially carry through your PhD worth working with that professor? Are there potentially other schools where you might apply in a year (or a semester) that would be just as valuable? At least that way, you could continue to pay off your existing debt and save more for the vow of poverty that is grad school.
Could you reach out to an undergrad professor and review your application weaknesses? The only reason I would even consider a masters is if I really thought I could enhance a mediocre undergrad performance, but if your performance wasn't poor, then would a masters necessarily buy you anything?