We walked over to the shuttle area and ended up with a guy who drove for ...."Go shuttle" or something like that. He was just waiting around there and when we talked with him he said $40 for 2 of us to the GCH. He did not hang around waiting for anyone else, so it was just us. He gave us his card and we arranged to be picked up at the hotel when we were leaving back to LGB for the same price.
Taxis have a $45 flat rate from LGB to DLR area, so that works, too. The way back, though, by taxi is meter (~$55) or voucher from DLR hotels for $50 flat rate. It's a different county and taxi company.