If you are using Customer Groups you can allow a customer to choose the delivery server for a campaign. Backend > Customer > Groups > YOUR GROUP > Servers Tab > Can select delivery servers for campaigns Yes/No.
To limit which servers they have access to you can assign only specific servers to any given group.
I'm not sure if you can select/edit the server after the campaign has started, but seeing as it isn't going anywhere you could pause it, copy it and start again.