I am wrapping up a Counseling Psychology PhD right now, and there is a genuine understanding on behalf of faculty that many students are intending to never conduct research again after graduating and getting licensed. This is in contrast to my friends in Clinical Psychology programs, where it seems like there is more pressure on students to emphasize their enthusiasm for research and downplay any interest in primarily clinical career goals. It is up to the student in an evenly split research/practice program to let faculty know what kinds of professional opportunities they are seeking.
I have conducted 3 years worth of student interviews and admissions process for my program, and the type of Masters a student is coming in with has never been an issue. If a student can communicate in-depth about the research they would like to pursue and how it's relevant to certain faculty members' research programs, then they are good to go.
Seems like you can't go wrong in finishing the current degree!
I entered a phd counseling psychology program with an MS in clinical psychology (clinical internships in assessment and counseling as well as research courses and projects- left with a publication) from another university. In my cohort of 6, I'm the only one with a clinical masters degree (others are counseling) but there are plenty in program with clinical. While there are clearly differences in our training and past experiences, we are all in the program and have good experiences to share everyone has past research experience too.