I'm aware of priority groups and planned to use them for part of this solution. Starting the app service is the tricky bit.
I think what's going on here is that the service is processing files on a shared file system and if the service is running on the backup service it will process those files at the same time that the primary system does resulting in either duplication or in the primary missing things because the backup grabbed the file. This seems like something the application should be able to deal with so I'm going to pursue it further with them.
Thanks for your help.
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Dave