Thank you for your response. I know it is a balancing act: on the one side is my academic work on the other my
research, job experience, etc. Does the latter tip the scale? Probably not, but it can maybe balance things out.
I have some specific Condensed Matter groups that I am targeting. I am thinking about opening up some kind
of dialogue about their research and maybe develop some kind of relationship. Could this also give me an advantage?
I would recommend for any student to get in touch with the faculty/group that they are interested in before applying to the school. But whether or not it gives an actual advantage is debatable and there has been many debates about it here on these forums!
It seems like unless the people you are in touch with REALLY want you as a member of their group and are able to convince the admission committee to give extra points or whatever to your application, it probably won't make a real difference. However, getting in touch with profs can help you prepare a stronger application. You can start a dialogue so you'd know whether or not you would be interested in what they are doing, and find out a little about how their program works. This could motivate you to write a stronger SOP or help you determine what that program values in its applicants and tailor your application to these values.
However, I should note that in Canada, if you are planning to apply there, getting in touch with people you're interested in makes all the difference. The admissions committee just makes sure all applicants meets departmental standards then forwards the applications to faculty members who individually makes offers to students that they are interested in. (This means that you actually are assigned to/pick a supervisor upon entry to grad school and start research right away). Also Canadian schools offer fully funded MSc programs (MSc and PhD are independent programs here) so if you feel like you need to do a MSc first, and want a fully funded program, consider Canada!