As someone who's spent their entire working life (up until last March) as a Financial Controller for a fairly large company, I've always been on the other side of the fence. There are a couple of things to point out here.
Firstly, if a company is of any decent size, they will normally have a Facilities Manager who will be responsible for ordering the work, and subsequently signing off the invoice. He is normally under pressure to obtain the best possible service at the lowest possible rate. In fact, the Facilities Manager at my last company was on a bonus for reducing establishment overhead costs.
Then, there's the purchase ledger clerk/superviser, responsible for paying the bills. These people are normally quite thick skinned, as they're inundated with calls and threats from credit chasing companies or credit control departments and are as immune to hard talking as traffic wardens.
When you send in an invoice, it's usually sent straight to the accounts department. It will be logged on the system and sent to the Facilities Manager. He'll possibly hold onto it for some time, just in case he gets any complaints about the clean from senior management. Eventually, he'll sign it off and send it back to the accounts department.
It will generally take a month or so from there for it to be included in a cheque run, hence the near two months wait. If the company is suffering cash flow problems, a small company will generally be pushed even further back in the payment queue.
If you become beligerant with the purchase ledger person, chances are they'll love the fight and it will become a battle of wills. It's much better (although never easy) to try and befriend the person paying the bills. I was FC at that company for 18 years, and the Purchase Ledger supervisor was there for 14 years. We were still never really friendly with each other, so it can be difficult. She was one stroppy so and so, who just about everyone in the company steered well clear of.