Just to clarify I am not interesting in chasing an H1B visa, I'd be happy with the normal post MBA work visa but I would like to extend it by doing a STEM degree. Is there anything like this that is 1 year long?
I have also thought about Canada or Australia but in my industry work experience in the US is highly prized.
Even though you may not chase the H1B - from the recruiters point of view - you are a risky bet. They realize that there is always a clock ticking with you. STEM OPT doesn't guarantee 3 years of work authorization. The way it works is all students (STEM or otherwise) gets 1 year of work authorization that the student has to request from USCIS indicating a start date. e.g. if you are graduating in May and anticipate getting employment in July. Then you would submit your request to USCIS to start the 1 year clock in July. Let's say if you don't get employment till Sept - well tough luck you have eaten into that 1 year clock and you have 90 days from the start of clock to find employment in line with your education - paid or unpaid.
After "1 year" you need to file again for an extension to USCIS - this is only available to STEM OPT. Please note that the USCIS can still reject your extension application citing reasons that your employment doesn't require master's degree or your employment is not in line with your education. So no - one cannot work in a McDonalds just to meet the criteria after doing MBA - I know because I asked this question to my school immigration officer during a seminar.
All the above - I mention - just to bring home a point that you become a risky investment for an employer. Now unless you bring some skill set that is just not there in US then only will a company be ready to hire you. Most of such jobs are high-tech and/or involve some way shape or form of analytics or awareness with coding.
By default most MBA programs are "generalist" in nature - even the specialist ones aren't deep enough to make you a subject matter expert if you are changing functions.
MBA/MS programs will accept you if you meet their criteria - Chinese/Middle Eastern students bring in lot of money for US tuition - this is common knowledge.
From a recruitment point - it may work in your favor if you find your way to China specific recruiting in US offices of Big 4, or something like the IBM Blue program. Companies like Huawei publishes several jobs for which they prefer bilingual Mandarin / English speaker.