Switching Tier 4 to Tier 2 during 28 day overstay

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?

Yes, you may (clause 101 of Tier 2 policy guidance and 245HD(p)).
Just make sure there are no mistakes at any end, as a refusal of an out-of-time application will not lead to right to AR.

Oh good it's a relief to get this confirmation. Thanks so much, appreciate you replying so quickly (especially on the New Year)!

Hi there,

I am so confused. Can anyone help with my case?

I had this job offer, working for the company as a part time employee on my Tier 4 (completed the course, got my certificate in October 2015) and the company will sponsor my tier 2 visa (planning to switch Tier 4 to Tier 2);
however, they've never hired a foreigner before so right now they are still going through the process of COS.
The home office decided to do an inspection on their COS application in early February but my Tier 4 visa is due on Jan 30th.

Before the company got their COS, i don't think they can apply for my Tier 2 in the UK??
Does that mean I need to leave the country on Jan 30th (This Saturday) and apply for Tier 2 in my own country after the company got the COS in February??

Thank you...
Best Regards, Kelly