A jeweler who purchases this gold from you will do what you can do yourself and save the middleman.

Send your gold to a refiner. They will charge you about a $25 assaying fee and then will give you options of how you want to be reimbursed for your gold--cash payment, refinery product, credit with the refiner, etc.

One that I've dealt with that has a good reputation is David H. Fell & Co. in Los Angeles. Their website--listed below--has information on their refining services and has a precious metals calculator to help you guesstimate the worth of your scrap.

Jewelers send their scrap and sweeps to refiners like this one.

Good luck.