Help Needed: Starting FT Directly After An Internship

I have an internship at a large independent advisory firm in New York City (EVR/PJT/CVP/MOE/LAZ for 2023 which I signed in April (through the moon excited and love the team)... and I have just realized that I can graduate in proper standing (PBK & summa) after next semester (majorly happy about this, since this will mean less tuition and boarding fees).

Although this is wonderful news, I am slightly worried as to what it means in regard to my career. I was planning on graduating in Dec of 2023, then taking some time to relax and chill before starting on cycle in June/July. I feel like having a full year gap between graduating and FT work might look bad, and honestly I would rather start sooner than later. 

If you were in my shoes, would you reach out to HR or the VP in charge of the internship and explain the situation in hopes of starting directly after the summer? [For added context, the group is unaffected by downward capital market activity (such as RX) and has been expanding head count]. I have heard it happened with a graduate at HL this year, but do not know how it would come off. I am worried that if I speak to the VP about it, it would look like I am assuming I will get a return offer which clearly is not a guarantee (so basically worried about coming off arrogant).  

If anyone is at one of these firms or has gone through this experience, please let me know and I will DM you.