Well, I got a response - as follows:
We understand you bought a boost and you can't use it with the character you want. Let us epxplain a couple of details that we search related to this issue.
If you recently applied another character service to your character (like a transfer or faction change), you must wait 72 hours before you can use a boost on it.
If you just purchased the boost or expansion upgrade in our Shop, you must wait until your payment is processed. This should take no more than 24 hours. You can keep track of the status of your order in your Transaction History.
I’ve issued a response clarifying that the payment was in fact, complete, and that boosts can apply to new characters too but clearly aren’t, along with a link to this forum thread. So let’s see what happens!