Assistant Prof. doing a post-doc or MSc at the same time
This is a bad idea. Regardless of the &quot;prestige&quot; of your current institution, you have a PhD and are appointed as an assistant professor. Therefore, doing a post-doc or MS will not advance your career but represent a confusing step backwards in your CV.
Why not instead contact the ivy league lab that offered you the post-doc and inquire about simple collaboration? You get to still help with the research and get out (hopefully) top-tier publications, they get to save the salary since they're not employing you. If things go well, maybe there could be joint grants in the future where your summer salary could be covered, or possibly including buying out some of your teaching load to have more protected research time.
I don't have direct experience, but I have some colleagues at teaching-intensive universities, and if you can involve your undergrads in your research and are able to put out high quality papers in respectable journals, the university will likely be willing to go out of their way to facilitate you and you could be on the fast track to early tenure.