Sounds like the rugs are not too large (if you were thinking of a bath).
Get large sheet of plastic out on a drive, put up some edging so it forms a pool, and immerse the carpet in water.
Either scrub manually or, and only if water not too deep and its 100% safe, use a rotary with a brush.
Let water go, keep flushing with a hose, push as much water out with a roller or your wand, lots of extraction.
Drying is the problem.
If you can get it up in the air on tressles or the like.