We also used Rainer, with David as our moving guru. It was an emergency switch from the provider we planned to use, and was put together for us in three days. (AKA, called them on a Wednesday, they packed us up that Saturday). The contractor they used on the California end, Sullivan, was excellent. We took the "slow, cheap boat" option. Our stuff was packed on the 22nd of April and it arrived here in the UK and was delivered in early July, as expected. David gave us the name of the boat and a link to a tracking site on the web and we watched its progress through the Panama Canal, etc. (Our stuff has traveled more than we have!)
The movers on this end were not as careful, and we noted that although we had "heavy" or "stack on top" stickers plastered all over the boxes of books and some of the more delicate stuff they were disregarded - we saw boxes of books stacked on top of the fragile, etc. We had very minimal breakage, and that was probably more caused by us not wrapping things as carefully as we should have. (We self-packed a few of the boxes.)
David was available to answer questions, was very soothing (we were in panic mode) and made some very useful suggestions to help us along. We had three lift vans and paid just about $5K from start to finish getting our stuff from SoCal to Scotland. The neat thing about using the consolidator service is they go by square footage, not by weight, and we had a LOT of books and other heavy items. Also, it would have been cheaper earlier in the year, or in late fall, but we were kind of locked in to when we needed to go. I definitely recommend them as a freight consolidator. You do have to remember that they just arrange everything, and have independent contractors who do the actual hefting, so it might be conceivably be possible to get a contractor on one end or the other who was not up to par. But we were happy with the service we got.