On F-1 OPT, Looking for H1b with non-profit under cap exempt status

I have a Masters in Divinity (Theology) from a US University. I worked at a hospital as a chaplain for 3 months on CPT and 9 months on OPT. I have three months left on my OPT.

I am looking for a hospital to hire me as a chaplain. Unfortunately my OPT timing sucks, so I cannot apply for the regular quota. Hence, I am looking for non-profit hospital positions. If I don’t find one in three months, I plan to change to F2 dependant on my husband’s student visa and continue to look for a job untill I find one.

Here are my questions:

  1. I found a non profit hospice who is interested in hiring me. They have never filed for H1b. If they agree to file a visa for me, is it possible for them to do so though they never filed one before? What is the success rate for the first attempt of a company to file a H1b?

  2. If I change my visa status to F2 and then find a non profit that is willing to hire me, Is it possible to change from F2 to H1b since I have a US Masters degree?

contact an immigration lawyer