score:2
I assume you currently are in a third-party country.
Schengen is independent of US. So
You have much more relaxed timeline here. Even if you are selected in the H1B lottery, actual processing to having your visa papers approved takes a lot of time (about 3 weeks if your future employer go premium, 3-4 months if not). Then the originals of the visa papers (I-129 and I-797B - approval) are mailed to you, only then can you go the consulate with your passport and apply for a visa. And being subject to a cap, you have until October, 1st to get it.