I've never had any problems carrying a backpack stuffed with lenses, bodies, speed lights laptop etc. through customs or immigration in the states.
Its better off in your hand luggage where it can be scanned rather than the TSA ripping your hold luggage apart to investigate it!
Get a decent, comfortable, backpack bag within hand luggage size allowance and don't let them think it might be heavy. Make sure your laptop is easily accessible for security scanning and has at least enough charge in the battery to boot up every time you go through security, just in case you are asked to.
ffs loose the water bottle, that will get you pulled!
I would pack the stand, brolly and softbox, gloves etc. in your hold luggage and anything you can't not be without or of significant value in your carryon.
Mini DV tapes, batteries, tape etc. can all be stocked up on in Walmart etc, unless you are going somewhere remote.
I usually carry 2 bodies, 3 or 4 L-series lenses,, at least 1 flash, battery grip, 6 batteries 2 chargers & 12v charger, cleaning kit, 8 CF cards, couple of filters, etc. Laptop, spare phone, portable HDD, Satnav & windscreen bracket, cables etc. Plus a magazine, paperback, pens & other travel essentials.
iPod & phone etc. go in my jacket pockets.
Anything that needs to go in the hold gets well wrapped up in clothing and/or put in a hard sided plastic container for extra protection. They will beat your luggage up, some airlines and airports are worse than others.
What are you using for power leads? I have sourced US mains leads for everything, usually, if you know somebody who works in an IT department they'll have a box of excess leads kicking about. Saves on weight, bulk, sticky out bits and the need for adaptors.
Hope that helps, even if your insurance covers it and they loose your luggage you're either going to have to buy or hire replacements if you want to keep shooting.
Have a good trip.