Yes that’s reasonable, probably even a bit low as it seems from what you said, the originating agent is in Asia, Japan to be specific? They will contract that out to a local agent of, I dunno, Atlas is a good possibility, or North American or Interstate, and the folks that come pack your stuff and take it back to the warehouse for a driver to pick up will be from a local affiliate of one of the Big Nationals. Joe’s Raceway Storage or Indianapolis Relocations or whatever. Or a driver may pick you up directly after your stuff is packed.
At the destination, delivery(which will depend on how soon they can get your small load on a truck going that way) it will be Capone And Sons or Windy City Storage and Transport or whoever thay delivers your stuff.
All of that on the assumption that your japanese movers are in fact in Japan. Yeah 3900 is reasonable. Get it in writing, there’s a very good chance the driver, if he delivers direct instead of dropping your stuff at a warehouse for the local folks to deliver, will try to hold you up for more money. Maybe not legitimately, but the driver who transports your stuff is probably going to lose money with a quote like that.
430 cf is good to know, sorta, but weight is the primary metric used for estimating price.