Scott,
I used to do this type of work but found most of the products ineffective.
I then found the 25%w/w permethryn which worked.
The fleas are relatively easy to kill , but it is important that a residual insecticide remains in the carpet to kill the new fleas which hatch from the eggs.
HWE in my experience does not kill the fleas.
I have not done anything like this recently , would probably recommend using a dedicated company.
Cheers
Doug