No need to mention them by name. Just use the AGPL, for they are all irrationally allergic to it.
EDIT: notice that usage of the AGPL produces the desired effect, while still being free software (which it wouldn't be the case if you excluded specific users in your license terms).
AGPL may go too far sometimes, as to intimidate companies from using an opensource project internally, and not necessarily as a (user-facing) service as in the case with the OP and AWS.
That's due to fact that AGPL's _user interaction_ clauses can be too vague in legal terms, in a way that many internal use cases could be litigated as a user interaction over a network.
AGPL in no way prevents anyone to use the licensed software. It just demands, like GPL, that modifications be made available to users, but in addition to GPL, extends this duty to the case where the licensed software is used remotely/as a service (rather than "distributed" to users for use on their own computer).
It won't take long until OSI heads come in and tell you that sort of licensing isn't "Open Source" (a commonly used term they bogusly claim exclusive control over). Who's financing OSI again?
Specially license tailored against every one of them, by name?