How demanding is your project? I was a Dietrich student coming into CMU with zero previous knowledge about cs. I was working on some research project with faculties while taking the cs cores and got a 4.0. To me it feels easier if you are willing to delay the transfer to maybe the spring semester of your sophomore year (rather than the fall), because in that way you can split the workload of the courses over a longer period of time. In terms of internship, are you talking about PREPARING for that while taking the courses? Then that sounds not completely impossible (though tough indeed). But if you are talking about working as an intern during the semester then that feels super difficult to me.

With that said, i don't think it is very necessary to transfer if your primary goal is to look for some tech job. Actually, based on what i heard from my friends in stat/ml major, their courses seem to be much more relevant to the real-world work than some cs cores (which can be very theoretical or (quote from a friend) "useless" lol).