It's likely not possible to open an account at another bank, wire all our money from SVB to there, and then wire the money to Gusto by 11am on Wednesday. So in the interest of ensuring employees are paid, the fastest option will likely be using SVB.
You're right that operating with two bank accounts now sounds like a good idea. We actually have that already because our structure involves a US parent corporation and a UK subsidiary, but the second bank account is in the UK (thankfully not with SVB UK, although ironically that's because we dragged our feet on moving to it).