One thing I'd recommend: have a way to invoice companies monthly who have agreed to pay you monthly.
For us: No invoice? No payment. (I'm not arguing whether that should or should not be a fact; I'm just stating that it is a fact for us and I doubt we're alone.)
Every non-trivial business will have accounting controls such that they won't pay out anything other than payroll without an invoice. And possibly a purchase order as well. Not doing this leaves you open to internal fraud.
(There's still a risk of external fraud, some big companies will pay invoices without checking ...)
They go through audits every now and then, where every single cent needs to be accounted for. "Oh, we ACH'd some money to that cool developer over there" doesn't fly.
Those audits may be for tax reasons (once you send an invoice, the payer can expect you to do your own taxes on that stuff, and they're off the hook) or to see what it's actually spending its owners' money on, which is especially important in public companies.
I don't work in finance, so for me the reason is "because finance won't pay otherwise", but I strongly suspect it's an anti-fraud accounting measure.
Would I pay more to be able to get invoices? No.
Well, technically yes, in the sense that I'm willing/able to pay $0 unless you can invoice, but otherwise, I won't pay an "invoicing fee" as a line-item surcharge any more than I'd pay a "printer paper fee" or an "electric lighting fee". Present the total invoice, and what you spend that money on internally is your business, not mine. If you need $1 for the invoicing process and I've agreed to pay $50, then $49 into one bucket and $1 goes into the invoicing bucket. I agreed to $50/mo, not $51/mo.
For us: No invoice? No payment. (I'm not arguing whether that should or should not be a fact; I'm just stating that it is a fact for us and I doubt we're alone.)