Q: I only want to ship one item (a rug) from the US to Israel, will I still need to pay all the same fees as if I sent many items. What is the best way to do this?

A: Individual items are usually best sent via the post office. Maximum package weight typically ranges between 15 to 20 kilos. If your rug weighs more than 20 kg., you can consider Heavy Weight air freight through one of the courier companies like UPS or Fedex. Air shipments are an expensive option.
Unfortunately, ocean freight of personal effects has so many one-time expenses, it is usually not worth sending via ocean freight. As you
suggested in your question - you are right, many of the expenses are "per shipment" regardless of the number of items.Customs clearance and e-transmission are just two examples of expenses unrelated to the shipment's size .
Another issue you must consider is customs expenses. Rugs are charged at the rate of 4% of the value, plus NIS 11 per square meter.
Finally, one last option, is to find someone who will take it for you in their lift, but keep in mind, you will still have to pay the customs fees mentioned above. (If the shipper is an oleh, there are limited customs exemptions on carpets.)