Schengen for Switzerland in Los Angeles with Advance Parole

[sarge_in]

I and my wife currently have the US Advance Parole card (the new combo card with EAD, the Employment Authorization Document) and made travel plans to visit Switzerland in couple months. However when we applied for the Schengen visa to Swiss Consulate General in Los Angeles, we were told that Advance Parole is not acceptable for applying there and we need to have a US visa or green card (both of which we do not). We tried explaining that the Advance Parole card an intermediate step of the green card process and is very comparable to the the US Visa for entry to US, and there isjust no visa issued for this purpose. It is also my personal understanding that this requirement is to ensure that people apply for visa only in their place of residence. And as I live and work in US (via Advance Parole), I should be able to apply and get a visa from US.
We did end up submitting the application anyway, but are not very hopeful that we will get the visa.

In the meantime, we did some more research with other Swiss consulates as well as other Schengen countries. Here is what we found out:

1) Swiss consulate in San Francisco - Talked to a Visa officer and she said Advance Parole is acceptable. However when she found out that I belong to LA area, she refused to help or provide an email confirming that Advance Parole is sufficient.
2) Swiss consulate in Washington DC - The person rudely refused to answer any questions once we told her that I belong to LA area.
3) Swiss consulate in New York - I have read messages on internet forums that they did accept Advance Parole in the past without issues. Have not been able to reach them directly yet.
3) France, Los Angeles - The website states categorically that Advance Parole is accepted.
4) Austria, Los Angeles - Confirmed by email that Advance Parole is acceptable.
5) Germany, Los Angeles - Confirmed by email that Advance Parole is acceptable.

In summary, so far only the Swiss consulate in our area seems to not accept Advance Parole. And the person even insisted that such requirements may be localized, and so San Francisco may have different requirements than Los Angeles - which sounds extremely suspect to me. I am at a loss on how to proceed if our visa gets rejected.

Has anyone else gone through a similar experience using Advance Parole? What are my options if my visa does get rejected? Any help will be much appreciated!