Cap gap extension for cap-exempt organization

Hello -
I work for a cap-exempt organization (university) which has filed for my h1 on July 17. My opt expires in Aug 17 and the processing time for h1 is about 2.5 months. My employers say since this is cap exempt organization, cap gap won’t work for us. is this true? they mentioned i will have to be in a work break until my h1 is approved. i did get my cap gap i20 from my college but my employer say we won’t take that as we are cap exempt org.

i do have receipt from my h1 filling - isn’t that enough to keep working until we hear from uscis on the case updates? is there any way to expedite the h1b case (they didn’t filed for premium processing).

Please advise what’s the best case for me to keep working until the h1 is approved.

Thanks in advance.

rk

Hello

I have a similar situation. What worked out for you? Please shed some light.