Wanting to maneuver to Research/Data Science, unsure of whether to accept another SWE internship

I'm a 4th year student in a 5 year BS/MS program concentrating in AI. I realized a couple years ago that private research was an actual career I could pursue. I understand that for many pure research positions you need a PhD, but I'd like to move towards some sort of research-oriented or research-adjacent job like Data Scientist, Machine Learning Engineer, etc.

However, I have two high-profile Engineering internships under my belt, which would be awesome if I wanted to pursue that career path further, and I'm getting a lot of interest for those kinds of jobs but I'm worried that if my last internship is another engineering internship I'll be "typecast" as an engineer and I'll never break out. I have a return offer for my engineering internship from last summer which expires Monday. Does anyone have any advice?

Edit: Another important detail that makes my situation more difficult is that I didn't get involved in research early, so I have no publications. I actually have a final project for my Deep Learning class which I think has a very good likelihood of being publishable work, and I need to write a thesis for my MS, but nothing is currently out in the world at this time.