If someone is going to come in to help with the carpet anyway, why not have them move the heavy furniture and take it all out? But wait until your insurance adjustor visits. If a spot is damaged the homeowners insurance will replace the carpet in the room, they'd never be able to match a little bit and the labor to do the patch would probably be more than to just redo the room. You should probably refinish the floor underneath it has been soaked with septic tank effluent.

For cutting out carpet use a box cutter and replace the blade as needed. My contractor had his assistants take out about 1800 square feet of old carpet when we started remodeling this house (replacing carpet with tile). They used box cutters and cut it into strips about 24 inches across the room and rolled it up. Took it out to the curb, and someone who recycles the stuff got it before the bulky waste truck got here to retreive it. The carpet is a biohazard, so be careful.