Trace Processes, Applications, active files, and modify registry permissions.

Find out what registry setting and file settings that you need access to with procmon, filemon and regmon and use the default windows tools called cacls and regini to change those so you have proper access.

Process Monitor v3.2 link

CACLS.exe
Access Control Lists apply only to files stored on an NTFS formatted drive, each ACL determines which users (or groups of users) can read or edit the file. When a new file is created it normally inherits ACL's from the folder where it was created.

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RegINI
Set permission on Registry Keys

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Alternative RunAs

1. Create a Scheduled Task in the task scheduler. The scheduled task launches the application. Set the task to run at highest privilege level.
2. Create a shortcut on the desktop of all the users needing to run the application. The shortcut ended up looking like this: C:\Windows\System32\schtasks.exe /run /tn "Name of task"

The only downside of this is that i need to create a separate task for every user, but I think it works just fine.