If anyone - Steve, Nigel or anyone else - can propose a way Labour could have called for any vote to remove Johnson that would be granted and binding, I'd be interested to hear it. The only other alternative is to do nothing.

Can't think of anything. But why try to remove him when he's already going?
Only his own party can request a vote of confidence in him. They did, he survived it.
Labour can try to bring down the government by a vote of confidence in the government. Which would (if successful) bring about a General Election.
Other than that, the question of who leads the Conservative Party is not really a matter for the Labour Party.
If you want to see it from a different perspective, the Conservative Party had no control over Blair handing control to Brown.