Though situation... Go sign-up for FundBox. Comes very handy for this type of emergencies. Also, check that there is not a chargeback on its way. This is a big deal that will spoil your day big.
Hope you be able to manage the crisis.
Although I cannot help speed up QB payments have you considered going local? When I was in retail we ran cards and had next day in our bank with fees only deducted once per month.
Alternately your local bank might offer ACH with next day deposits for a reasonable charge
I'm sorry to hear that your first transactions have caused a stressful situation. That's definitely not something we want to hear from our customers. Let me see if I can provide some context. For customers who are new to Intuit, the first transaction (or, if there are multiple transactions) or first batch may be held for approximately 3-5 business days. An internal review is done at that time because you are a new business with us. After that initial hold, transactions are deposited to you based on your account deposit time. Generally, this will be 2-3 business days for credit card transactions and 5 business days for ACH transactions.
However, there may be other reasons that transactions may take longer; for example, suddenly processing $20K in one month when a customer had processed $2K may trigger a risk review, where we will hold funds while we review those transactions. Once those transactions pass review, the are generally released in 24-48 hours (again, it may be longer; this is a case-by-case basis). If you haven't received an email regarding these transactions, it is likely that you haven't received the funds yet because of the initial hold.
For further information on holds, I would direct you to review the merchant agreement agreed to at the time of sign-up. Here's a link: Merchant Agreement
If you have further questions about the specific transactions, I would reach out to the support team directly so they can review the account. Due to the public nature of the community group, I can't go into specifics.
Payments support can be reached here: Payment support
I hope that helps!