I want to do a PhD but I think I need more supervision. Should I be more direct in setting up more frequent meetings with my PhD supervisor?
If I understand it correctly, your funding comes from one source, but your doctoral studies are somewhat (at least) independent of that.
You need to satisfy your PI and others in your funding stream that your work is good, but since this isn't a permanent position, your primary focus should be on a productive relationship with your PhD supervisor.
So, yes, frequent meetings with the supervisor but without neglecting the others, unless you can find a different funding stream.
Focus, primarily, on long term goals. If the job in the lab supports that, all the better, but the degree is primary.