Tell your client that as a consultant your fees would be subject to a buyout schedule as follows:
Send invoices monthly. If they pay your invoice, no problem. Each month that goes by they would pay an increase according to the schedule above.
This gives them the ability to pay you back without giving you equity, but recognizes the high risk you are accepting.
At the end of the year whatever is left over will be treated as a convertible note towards equity. The buyout option would expire. For instance, if you billed them $50K in August and they never paid you, you would get a $100K convertible note in September the following year.
The same rules would apply if your client is using the Slicing Pie
model, but at the end of the year you would get slices in the pie instead of a convertible note.