You’re information is more or less accurate.
Regarding point A - the 2 year home stay requirement depends on which country you are from. The UK and most of Europe/the Western world are exempt from this, unfortunately most of Asia, India and the East aren’t which is probably why you couldn’t take the offer of extending your time. It’s just another one of those rules that the US enforces to make it difficult.
Point B - This is the difference between being a J1 intern and a J1 trainee. You can be a J1 intern up to year after graduating. You can be a J1 trainee with one year or more professional work experience in your home country in the same field. Proof of this would be pay stubs etc.
A J1 trainee is valid for 18 months and is more what Bepster was talking about when taking it as a trial period. I did forget to mention the home stay requirement so it’s worth double checking what countries usually get this enforced. Sometimes though this can be at the discretion of the interviewer at the US embassy - however it very rarely happens to UK/European citizens.
Unfortunately the J1 option isn’t for you and I’m sorry for the false hope. Although it sounds like you made some great connections through your original internship so if you have completed your 2 years in India why not reach out again? I’m not sure if the 2 year stamp may impact your chances of getting a student visa also? It might be worth reaching out to an immigration lawyer in the US as my knowledge of the situation is running a little dry!