Do you think there should have been a contrivance to pre-empt the Eagles question?

[Inziladun]

Originally Posted by Marwhini

'Twice you have born me, Gwaihir my friend,' said Gandalf. 'Thrice shall pay for all, if you are willing. You will not find me a burden much greater than when you bore me from Zirakzigil, where my old life burned away.'

'I would bear you.' answered Gwahir, 'whither you will, even were you made of stone.'"

This implies that not only was their absolutely no reluctance by the Eagles to act on Gandalf's request, but that Gwaihir seems to be in some sort of debt to Gandalf (else what is he "paying for" in 'thrice shall pay for all'?).

I wouldn't read too much into that line of Gandalf's. It's used other times, by other characters. There's Bilbo:

But 'third time pays for all' as my father used to say, and somehow I don't think I shall refuse.

The Hobbit Inside Information

And Sam:

'Gollum!' he called softly, 'Third time pays for all. I want some herbs.'

TTT Of Herbs and Stewed Rabbit

I think it likely Gandalf had just picked up that saying from his long-time association with hobbits.