The invoice is live when you create it.
If you send an invoice and you get paid for it, revenue will be recognized on your financial statements, either on the invoice date (accrual) or the payment date (cash), or the invoice date if there is a pre-payment (cash or accrual). There isn't any way around that.
In your case I think your invoices should be dated at the beginning of the service month, as that is what they are for (you won't earn the income until then, and your customer knows - more or less - that if they cancel their contract you won't be expected to and they won't be expected to pay.)
If you must send them early, you can create a custom field on the customer list and then add it to the invoice, name it something like "Billing Date", and enter the billing date (9/1 in this case) in the field, but use 10/1 as the actual transaction date.
You can then use the invoice layout designer to position the field as needed, next to or in place of your internal transaction date.
