> As long as you're organized and quantify every line item and have proof of sign off on things that increase scope and have emails to back them up

if you're doing this then you likely will never have a problem no matter how much the invoice is. Organization and authorization (sign-off) is the key, if there are no surprises then they'll pay every time.

> The best are boring large to mid size companies.

I agree, Accounts payable doesn't have any emotional attachment to any amount at these companies. If the invoice has the right approvals/criteria then a check is cut no matter what the amount is.