You totally messed up yourself!

What you said and done is totally wrong and unnecessary.
1. Post-doc h1 in university is not subject to H1 quota, so you do not need to worry about quato at all.
2. Even in the rare, almost impossible, case this position is subject to quota, there is still H1 quata available for person with advanced degree. Since you are postdoc, you must have PhD degree, so there is still quota available. Don't say you only have bachelor degree and try to be postdoc!
3. Even if you need H1 subject to quota, as long as you submitted the application before uscis runs out quota, you can get it. So it is totally unnecessary to use 加急 to catch quota.
So, what you did is totally unbelievable and unnecessary. Do a little bit research yourself and you can easily get the answer. If you can't research to get those answers, I seriously doubt how you can ever do research in your own field!