Wouldn't trust coating over the HF powder on the cart. Strip and recoat is the only way to go. As said previously, prices will vary depending on size of shop, equipment, and expertise. Our shop can't compete with a guy working in his garage in the evenings as he has no overhead, payroll, etc. -conversely, I can't compete with huge automated line places on jobs of hundreds to thousands of pieces. Tool boxes are a pain as there are lots of pieces, and lots of sides, corners, etc. takes longer to clean, strip, and coat. We still do them. The stripping is the most costly part of it. We have the ability in-house to thermally strip it, so in a matter of an hour or so, the existing paint/powder is reduced to dust. Blasting time is reduced to minutes in lieu of hours. Not too many shops have this ability. There are some stripping outfits that can either chem strip or therm clean. Here locally, Ready Strip offers these and other stripping solutions, although most strip places with thermal burnoff ovens typically require a $800 min/load.
A HF cart with a drawer or two, lid, and frame if stripped would run about $250 in our shop - and less if previously stripped. Full snap on boxes can be 2-3 times that depending on size and drawer count.