If you can sort out a "Type 1" client (ref your definitions above) you can sort out anyone. I have taken on one myself - except it's not a shoe box, it's a blanket box, and his primary filing system seems to consist of the floor of his Land Rover.
You need to provide this sort of client with a straightforward system - procedures that are both portable and which are really easy for him to use - aimed at channeling the paperwork to you sorted into the various streams that you need to do your job - invoices, receipts for cash transactions, statements from bank and credit card companies etc etc etc.
You can't sort his books out unless he plays ball and gives you what you need. (And you know what you need so it's you who must tell him). On the other hand, if he wants you to do all the sifting and sorting for him, that can take an awful lot of time, and he'll going to have to pay you to do so.
