@Chase One approach you could use is having your restlet under a normal Websrvice/TBA role, then when you get the request from the external system to update this customer or customers and you off load that data to a Map Reduce Script, the advantage of that is:
1- Your restlet would be immediately ready again(because it send the processing to the background).
2- A Map Reduce script deployment have the option of: Run as... which mean you can make the Map Reduce Run as Administrator...