SEVIS Transfer after VISA Expiry and 2 month GAP to start new college

[satsL]

Hello,

I'm currently working on STEM OPT extension and my EAD expires on June 28th, 2018 and F1 Visa has already expired on December 13th, 2017. I'm working for a non-profit organization and they have applied for H1 with start date as June 1st, 2018 and have received RFE. Now I don't wish to submit RFE(submission deadline- August 27th, 2018) and continue studying MBA at a different school. But the start date of the MBA program is on August 20th, 2018. Below are my questions.

 

1. Can I transfer my SEVIS to new School and stop working from June 28th? and Will I be out of status as my visa has already expired and OPT expires on 28th and the start date is on August 20th.

2. Should I work until August 19th as I have CAP GAP extension and then transfer my SEVIS and withdraw H1B petition.

 

Visa expired on  December 13th, 2017
STEM OPT EAD expires on    June 28th, 2018
Sart Date of MBA program is on  August 20th, 2018

My current University has confirmed that my SEVIS has updated with CAP GAP Extention until September 30th, 2018 but I'm skeptical whether I'm eligible for CAP Gap extension because my H1B is filed under CAP exempt as I'm working for a non-profit organization and start date is June 1st and not October 1st, 2018.

Start date on H1B petition - June 1st, 2018
CAP GAP extension till September 30th, 2018
Deadline to Submit RFE August 27th, 2018
 

I would like to know what is the appropriate time to transfer my SEVIS to new School, quit working and when to withdraw my H1B petition without any violation.

 

Appreciate your help on this!