I've had some luck with discounts for lump sum payments on past due accounts. But you are right, if he don't have the 60k then he probably don't have 40… Every customer is different and you need a few options to pull from.
Since the COD business with this guy is "worthwhile" push for a payment plan that gets him paid up in a year. That'd be $5000 in addition to the COD orders each month. Basically you’re reducing his credit limit $5k/month. Grant him a reduced interest rate or some kind of discount for sticking with the plan. You'll have to keep pushing every month or he won’t stick with it. Of course he may start favoring a different vendor depending on what they let him get away with.
Make sure your people have no grey area with his credit limit/terms. I went to a pre-bankruptcy mediation one time for a customer who owed us $9000. The owner of another company was there and had just survived treatment for brain cancer. While he was away from the business his staff let the customer get into them for $250,000.

And then we listened to the bank make it clear there wasn't going to be anything leftover for us unsecured vendors when they were done with him...
I agree with Greg that willingness is a factor. I’ll work with someone that makes an effort to send some dollar amount each month towards the old. We had one guy that always kept a $20k recurring balance. He paid just enough each month to cover his new purchases. It always pissed me off when I heard people say he owned all kinds of land and has a new piece of equipment or pickup on the yard every time they visited. Basically we were carrying his balance because he was a lazy bookkeeper.
Good luck!