It seems like you could spend a lot less on the bike shipping if you pack and reassemble your bikes yourself. You'd need to remove wheels, seat, pedals, and rear derailleur. You'll also need to loosen the handlebars. You'll want a spacer to keep your fork/frame from being bent while the wheels removed (sometimes you can pack without removing the rear wheel). You may be able to get a box and plastic spacers from a local bike shop for free (used packing materials from bikes they've received). Additional bubble wrap and fill material available as ordinary shipping supplies would also be useful. You can probably get the bike shipping down to $2-300 total.
Alternatives for moving all your household goods are varied. You can rent a truck one-way (U-Haul, Penske, etc.) and do the loading, unloading, and driving. You can hire a transport service to drop off a truck trailer or shipping containers (U-Pack, PODS, etc.) that you load and unload, but they move. You can also hire full service movers. Costs of options will depend both on distance and on demand in the areas you are moving between.