OP: take the rug to be cleaned. It’s a size that is manageable and will fit in your car.
I have an antique Kerman rug, which I have professionally cleaned by the folks who sold it to me–they sell a wide range of Persian rugs and have people who do cleaning and restoration. It’s their only business. Someone spilled wine on the rug at a party and I immediately called the owner who told me about using a spray bottle with a vinegar/water combination. It worked like magic and saved the rug.