H1B grace period is over but no H1B transfer filed yet, I-94 is not expired though

[vsrupa7]

My H1B 60 days grace period ends on June 14th 2020 where as my H1B expiration date is 06/28/2022 and on my I94 it says: Admit Until Date : D/S which I believe will be the same as the H1B expiration date which is 06/28/2022 (please correct me if I am wrong)

I heard/read that we can stay upto 180 days until I-94 expires. Considering this, can I stay legally in the US until Oct 12th 2020 as it the 180th day after my H1B was revoked? Does that mean I have until Oct 12th 2020 to find a job and file for H1B Transfer however I have to go out of country for the visa stamping if the H1B Transfer was filed after the 60th day? Please let me know if this is right

Please let me know what options I have. Any help is much appreciated! Thanks in advance

[R78]

Once terminated, you have 60 days to find another job and file for an H1 transfer. This enables you to start work as soon as the receipt is obtained from USCIS.
If an H1B is filed after 60 days, you cannot work unless the approval notice is sent to you.

If you want to stay in the US beyond 60 days to find a job, you may do so. However, you must file a COS from H1 to B2 before the 60 day grace period ends. It can be done online.
This is the right way to do it and will ensure your immigration record is clean !