I don't have an answer for you, but I do have some food for thought . . .
I applied to do a Masters in Robotics at CMU . . . they rejected me on the reason, paraphrased, that 'engineers make bad scientists, they just like to build stuff'.
So, I took the first decent job offer I got a few months after graduation. With just a bachelors. Turns out the job I got was my dream job. I got paid to do robotics research for the US government! Normally, this stuff is reserved for PhD's (I'm surrounded by them), but robotics engineers are extremely hard to come by - especially ones willing to work on a government salary. So I was in high demand.
The pay scale works like this . . .
University Research . . . paid beans and worked like a dog
Government Research . . . paid ok, easy work
Industry Research . . . paid really well, stressful deadlines on occasion
So why work at a University? Well, you get a fancy schmancy paper that says your a doctor. You also get to focus purely on science, not having to worry about profitability or the usefulness of your work for the military. And some professors even like to teach. Other Professors like the free skilled labor called Masters
Now, I've spoken to a few people who went to earn their PhD at CMU . . . they all flatly regretted it and said 'don't do it'. They recommended Masters only, unless you want to be a professor. It's 7 years of hard work without a paycheck. You're guaranteed a job after graduation, on the assumption you didn't waste those 7 years on a useless project. You are only 'over qualified' if you want a PhD salary but don't know any more than someone with a bachelors . . . and yea, there are PhDs like that.
Now, I don't know about other schools, but CMU pays your entire tuition if you do the PhD program. But you must pay the tuition if you do the 2 year Masters program.
Now, if you decide to work for the government, you got two options . . . contractor, or Fed. Contractors get decent pay. Feds get not as good pay, but really good job stability and a nice retirement package after 20 years of service. If you choose Fed, you go on the pay scale. Higher your degree, more money you make. I did the math, and after ~30 years of working you'll make about the same no matter what degree you get (because earning a PhD is 7 years without pay). However, if you don't have a good degree, it's harder to get hired. I got hired because I got skills
Now, about 'engineers make bad scientists, they just like to build stuff' . . . two years after getting hired, I wrote a paper and published at the worlds largest robotics conference, ICRA. Out of 1000 papers, our team ranked #1 . . . I was first author . . . and one of the people who rejected me was there to see me pick up the award. Redemption, hehe.
Anyway, I like doing research for the government. It doesn't pay as well as industry, but I got freedom from profitability and get to build stuff (I do like to build stuff). I just don't get a fancy schmancy degree that says I know it all . . .
So . . . food for thought . . .