Happens to me, too. Though less now than before.

What to do about it? Therapy seems to be the only choice if you want things to change. The most effective treatment for me has been brain spotting, which is kind of a blend between EMDR and SE.

You don't have to integrate to be co-conscious. In other words, you can learn to be aware of what is going on with more than one part at the same time. For example, I am now able to say that Marie feels a little lost, Korina feels strong, most of the others feel bad for my t whose brother just died. I learned to be co conscious with talk therapy. I am not completely co conscious now, but am a lot of the time. I have been in therapy for 9 years and so far only 2 parts have integrated. They just did it without me really noticing until it was done. I do not have the goal of integrating, although that is fine if it happens. My goal is to not lose time and to not switch in public. Which sounds like it might be your goal also.