The majority of insurers in my area have been attaching "mold, mildew, and dry rot" exclusions to policy renewals for several years now. The "something smells funny so I had to replace my carpet" claim was costing the big bucks.

If the carpet was wet long enough for any mildew to get started, your chances of a successful "rehabilitation" of the old carpet are pretty small. Bleach will "stunt" molds (maybe make them whine a little) but don't reliably kill all the spores - they'll likely pop back at the first opportunity. Bleach will kill the bacteria that are present, but won't remove the nutrients that have "silted in," so any re-inoculation with any bacterial agent will likely "bloom like the lilies in springtime."

There are "mildewcides" that could be applied, but the ones that are likely to be fully effective can be a hazard (especially to small children and pets) since they have to leave a persistent, toxic, residue to have any extended effect.

Even the cost of a decent "electric shear" or other "sophisticated tool" is likely to be as much as it would cost you to get a replacement "throw down" carpet, if you buy remnants from a typical carpet source, or if you go to one of the "salvage sales" or other discount outlets.

Of course, consider your options; but from your description my choice would be 1.) get it out using the simplest and quickest method available. 2.) throw it away. 3.) replace it with something that doesn't go under all that heavy furniture - for next time.

(You do need to get the pieces out from under the furniture, or they'll likely rot the furniture bases in short order.)

John