After you have created the task to run Everest elevated at startup, did you disable the original startup entry for Everest in startup programs? If not, that one will still load at startup with the UAC prompt.
If this is the Task Scheduler trick that you used below, then I do not of anything that you can try other than turning UAC off. You might contact Eversest to see it is a known issue, and if they have a update or workaround for it.
1. For how, see: How to Create a Task in Vista Task Scheduler. NOTE:Create a task to Start a program (Step 20) with the program's EXE file, check Run with highest privileges (Step Four), and have it set to be triggered at startup (Step Five).