Geez, what a mess!!
I have never dealt with such a crappy situation
so here's a few thoughts off the top.
Raise holy hell with the city a see if you can get them to do it for free.
Call a local septic system company for ideas or bids.
What ever you do be careful, you have no idea what kind of bacteria and disease is floating in that sludge.
Certainly $$ potential here...Private client? National?
Nats Pay $75-100 for a soiled toilet...say 3 gallons in a toilet. Calculate gallons on the floor and go from there??
$25 per gallon...there's 7.48 gallons per cubic foot
4114x.125 (1.5 inches average is .125% of a cubic foot)=514 gallons
If you're working for some nat taking 30% that leaves you with 9k...maybe a little steep...maybe not. After all it's raw sewage....and after the bulk is gone it will have to be cleaned and disinfected.