Re: Problem is...
"wherever possible we want our teams at the FT to migrate to Amazon Linux, because it saves us money – and we have a website that shows each team how much they would save"
Aha. So instead of telling the team to migrate to AWS - which would be old-fashioned top-down management - you drop not-so-subtle hints that they should do so. Also include implied threats if they don't - in this case, budget problems.
Let's have a new buzzword for this: Passive-Aggressive Management, or PAM for short.