I am a first-year PhD student, and as the title suggests, I've told my department that I'll be leaving the program this summer (that is in one month), but now there's a situation that I have a reason to change my mind. To do so however, I would need to have some discussions with a potential advisor, as well as the department. I was wondering who I should contact first. In addition to the context, which I explain below, the subtlety is in the process for changing my status back to what it was, because now my department assumes I'm leaving and stopped doing some of the procedures they do for other students in the cohort. So, to decide that I'm staying, I would need to get an approval from my potential advisor that he could indeed be my advisor, and get the approval from my department that I could stay and that they allow me to work with that advisor, who is in a different department, but within the same division of the university.
So my question is how should I proceed with this? Should I first ask my department if this is at all possible, or should I first talk to the potential advisor? I think this order might matter, given the short time I have left, the fact that me staying here is critically dependent on this particular arrangement to work, that I would need to decline a different PhD offer I've already accepted (see the explanation below about that), and the whole context below.
I would much appreciate some comments on advice on the question above, and also any suggestions or comments on any point you think I might be missing, or on the potential costs of doing or not doing such a change of plan at this stage.
Two possibly important points: 1. The country is the US. 2. I have followed through with all the requirements so far and would be in good standing to proceed to the second year if I was staying. The main deviation from the PhD timeline is that other students have made advisor-advisee arrangements, but since I told them I'm leaving, I haven't. The arrangements were finalized very recently, but the process started a while ago, so I don't know if it is too late already for that or not.
Here is the context if you would like to know more:
Why I was/am leaving the current program and starting a different program: I plan to go down a path that would be impossible to follow without at least some outside of department advising. My department was in principle ok with that, but the other department where the faculty I was interested in working with is in was not. Meanwhile, I already had a PhD offer to go pursue my area of interest at a different university (starting from first year again). So it seemed reasonable to take that offer. (My area of interest is quite different from the field of my current department, but the work is somewhat interdisciplinary, so if I could find an advisor, it wouldn't be too unreasonable to do the research I like as a PhD from my current department) That's despite the fact that staying in my current department was my strong preference, for multiple reasons, if I had some reasonable hope that I could have the career trajectory I like to have.
What has changed: I found out that a professor whose work I'd been following for quite some time has moved to my current university from where he was before, and he's also in a new department, which has much closer relationships with my current department. That means the bureaucracy, the administrative matters, funding, etc. are unlikely to become an issue (unlike the case with the other faculty I wanted to work with), as long as the professor accepts to work with me.
Why I hesitate and care about the order that I contact the professor or my department: First, I have already bothered my department way too much (including a whole series of troubles I made for them that are unrelated to this). Second, I would need to talk to the professor I'd like to work with and see what he thinks about my plan and working with me before I can decide for sure if I want to work with him. On the other hand, I'm already way past the decision point; I have already accepted a PhD offer from elsewhere, and regarding my leaving, it seems like that ship has sailed. I know I'm going to embarrass myself by bringing up the possibility of this change of decision, so I don't want to burn bridges, make a fool of myself, and disappoint everyone, if at the end of the day there's no point in doing this. I'd appreciate some insider insight on this since I don't know where departments often stand in this type of situation, and how strictly they have to follow the April 15th agreement (if at all, given that it's not between two PhD offers, but between a department I was already in and a PhD offer).