I've shipped out many items of similar weight and size via USPS, Fedex and UPS. Price range always was $20-$25 especially sending items to the east coast. And that's before shipping supplies. It's cheaper to ship within CA and to NV but even then not by much.
I tried fitting the RMS box in USPS priority flat rate boxes of two largest sizes for you but it didn't fit, unfortunately.
$10 sounds too good to be true. Do you have an account with one of the currier services? Regardless, I'd rather sell it locally or just keep it for future use.
Used a UPS shipping cost calculator and what I got was $21.99 from LA to Woburn. Quote was based on RMS box dimensions, weight (4Lbs) and your location. That doesnt include the cost of buying a box for shipping,