Suggest a cross country mover?  

moving sucks
yes...I don't think the carrier is as important as your preparation for the move. I have moved four times in the last six years. Each time was by a professional moving company, paid for by corporate relocation deals (they pay).
Here are my thoughts:
1. Most moving companies require third party crating. Small price to pay.
2. Buy pizza and tip well the first day. They will get the message that you will treat them right if they treat your stuff right.
3. segregate the important stuff and pack it last. Just put it all in one room and ensure that you tag and record each box leaving that room with values.
I only had one claim, and with a little negotiation, I was able to get most of the loss back.
That said, I don't think the carrier is that important, as they all "contract" locally with people to pack and load, and "contract" out the drivers. The biggest factor is probably how well you prepare, document, and prepare your valuables.

United
We had a bad experience. We were part of a consolidated load, so we only had part of a truck. The guys that packed our stuff squeezed us in so tightly that we had a fair amount of damage. Thankfully, nothing precious or irreplaceable and we did get a refund. I'm not sure that should be blamed on United Van Lines or just he local office and the monkeys who did the loading. But word to the wise if you go consolidated, pack the bujeezus out of your stuf and annoy the loaders and watch what happens to every piece!

I think
You should use those moving pods.
Never tried it myself, but they look cool.

Expect the worst.
I had nothing damaged. A miracle since it was all handled by Baboons.
I started packing a couple months in advance and printed color coded
labels so that when things arrived, they went to the correct rooms and
the 50 misc non-important boxes were stacked in the garage.
A language barrier made that challenging. The valuable and delicate boxes
had giant hot pink labels with up arrows! Funny how two of those almost
left with the moving van. (thieves). I'm glad we checked. We may have not
missed them for weeks.
This past Jan month, i had a POD delivered. We needed to clear out downstairs
to do some renovations. I would consider it in the future if we ever moved
again. Same price for one day or i month. You can pack it yourself at your
leisure. Boxes are out of the house and ready to go instead of double handling. (mine just sat in the drive full of chairs)
They will store them and send to your destination when you are ready.
I bet they also have a crew that will come and help pack if you need it.
Craigs list is a great place to get boxes from someone who has just moved
to your area. We got ours from a friend who recently had moved and then
they went to a friend who moved to Texas. Rent-a-crate is another option.
http://www.rentacrate.com/

Thanks for your experiences
If I can decide to do this move (still up in the air), I was planning on either using Allied or American Van Lines. I intend to pack my clothes, towels and sheets in heavy-duty large black plastic bags with those permanent plastic ties (the kind you have to cut to loosen). I moved 5 blocks and used a Pod for the non-breakables with no problem.
If i can get the right sized boxes, I can also pack my books, records, CDs and DVDs myself too, and save some dough.
If I do this, what i don't want to do is crate furniture or pack breakables....I'd rather pay to have that done by professionals.
I've yet to fly down and scout neighborhoods and look at houses. That'll happen in April.