Hello! So I'm a non-EU citizen whose Tier 4 student visa will expire in a week's time on January 8. I am potentially receiving a job offer from a company which did not put their job advertisement through the RLMT (I say potentially, because the company's HR initially thought that they could not sponsor me due to that RLMT restriction, and I was unable to let them know that my student visa exempts me from the RLMT before they closed for Christmas).
So right now, I'm trying to plan for the second worst case scenario (the first being that they've offered the job to someone else before closing up for Christmas

): that they offer me the job after they open on January 5, but that I am unable to make the application to switch to the Tier 2 visa before my Tier 4 visa expires on January 8. I've carefully read the policy guidance notes, and I
think it looks like I can pull this off, but I'd like to seek clarification in case I missed anything major:
Am I still eligible to switch from a Tier 4 to a Tier 2 visa within the 28 day period of overstaying, if the company that would be sponsoring me did not put their job advert through the RLMT?