I see the point for the 'Stick' way of handling late payment, but how about trying the 'Carrot' approach ?
Work out your fees, add the amount you would charge for late payment, but add a discounted price, (the price you really wanted in the first place) for 'early settlement, which can be any reasonable period you wish to choose.
We all get a similar situation every day...the shops are now beginning to offer, 'Pre end of event prices'.
Buy now for ONLY
£299, after event price £799
and even if your as cynical as I am, you have to admit that it works.
Hope that helps.
Les