Did Griphook double-cross Harry and Co.?

Well I’d say because after all, he’s still a goblin. It is in their blood to protect the treasures of their clients. No matter what the situation, it goes against their nature to break inside of someone else’s treasure, someone’s treasure they’ve sworn to protect.

So when he leaves the trio, he not only retrieves the Sword of Gryffindor (which must have been an infamous artefact among the goblin community as a treasure unfairly stolen), but also saves one his client’s vaults from being looted. Even if he hates Bellatrix, it’s still bad reputation for the bank and the goblin species if they come to know that a goblin helped in a robbery. They don’t particularly hate the Death Eaters too, because they were neutral in the war.

Griphook doesn’t double cross them as you say in the question. Because the trade was to help the get inside the vault not get them out, or leave them to die inside for that matter.

He left Bogrod, because in Griphook’s eyes, it must have been a good deal. Sword of Gryffindor and saving the bank from an embarrassing robbery for the exchange of life of one of plenty of goblins. The reason to the disregard of Bogrod’s life could be due to the fact that they all work in a single place, and there might not be need for so many goblins, leading to salary dilution. So he didn’t particularly have any love for Bogrod.

Goblins are very cunning. When the trio plot to betray Griphook, he must have found out about it pretty quickly. That’s why it’s mentioned a few times to never double cross a goblin and how risky it is to trade with them. That is also why people keep their distance from them. So Griphook would have then plotted a plan of his own to get a better deal than the one they were giving.