I don't know if you read my other thread, but flying Delta into Manchester isn't feasible for us. I am like you in that I don't live near a gateway city. The only gateway cities you can take into MAN with Delta is JFK or Atlanta. Here are the problems I have with them:
1) They require 4hr minimum between connecting flights. Because of this, and your distance from ATL or JFK, you will be unlikely to get all your traveling in one day. So you will have to spend the night in either JFK or ATL. This screws with your tick/flea/tapeworm treatment, so you will likely need to track down a vet in either of these cities.
2) If you could manage to get flights in the same day, into a gateway city, then you are responsible for picking your pet up at the domestic cargo terminal and then checking them into the international cargo terminal. I don't know about you, but I don't want to be dragging around my carry-on luggage, leaving the airport terminal to get taxis to the separate cargo terminals, and then heading back to the airport terminal and going back through security. The only way around this 'inconvenience' (the word the cargo rep used), is to hire an IPATA agent.
I had much better luck with Continental, going through EWR. If you can get to Vegas, it looks like you could use BMI. Use that link that the previous poster linked to determine which air routes are available to you, then call the airlines and find out their procedures, costs, and what routes into/out of what cities to get you to MAN..just make sure you are leaving from one of the gateway cities.