Physics Undergrad at Liberal Arts College, Transition into Engineering Degree?

Yes, I do have some research experience. I worked in my professor’s lab over the summer and have a poster written about the work I did. He did say at some point that it would be written up and have my name on it if I wanted as 2nd or 3rd author, but so far nothing has developed further than that.
The problem with the research on campus is that there is only so much of it in a school where only 1800 students attend. One prof works with Bose-Einstein condensates, another with trapping atoms with lasers, and my professor works with supercooled nanomagnets. Others work in biophysics labs. None of which exactly are “engineering” projects - I wouldn’t be able to get a feel for engineering here at a liberal arts college no matter how hard i tried.

Do you really think a degree in master’s would be more beneficial to me than a bachelors? I mean, either way I would have to take a semester or two after graduating to catch up. The advantage of the dual-degree program (basically just an extra year of undergrad) is that I would be exposed to engineering earlier on, and I would really get a feel for whether I want to do this as a career. After having made that decision, I could then apply to grad school and theoretically still graduate at the same time as if I had just applied for a master’s program straight out of Amherst, then had taken a year to catch up on undergrad engineering coursework. Or I could just work for a few years and then go back for my masters. The dual degree would give me flexibility in those paths.

Around what do you think I would have to bring my gpa up to to be competitive/above average? It will be pretty difficult to get A’s in advanced electrodynamics and Quantum Field Theory… although I’d expect earning a 3.6 cumulative total gpa wouldn’t be too difficult by the time I graduate considering my relative ease in the humanities courses.
Do grad schools care more about the physicse gpa or the cumulative gpa?

By the way, thank you for your response @boneh3ad‌.