Thanks for the info!
Unfortunately, I don't have that outer plain box. I bought it at a retail store, so only the fully logo'd, big picture, white iMac box. I had prepped it for sea shipping, so it has lots of extra bubble wrap and popcorn inside, to protect the screen, etc. No open spaces left inside. I hope it's safe that way.
The rates at the Meest website seem pretty reasonable, but that doesn't count insurance or any customs fees. I'm going to be declaring everything as personal effects and household goods, which is true. None of the boxes will be over 70 lbs (Meest says anything over 70 lbs will be counted as commercial, and must have customs paid), so hopefully it won't cost a huge amount.
I'll be talking to Meest in the morning... the shipper I had arranged before leaving is still wrangling with Ukraine customs and port authorities, while my things sit in storage in California for over a month.
It was when they said they're being told they can't ship to Odessa or Kiev, and that they have to ship to St. Petersburg first, I knew it was time to find another shipper!
I guess just like everything else, it's good to find someone experienced in dealing with Ukraine...
