That's actually exactly what you should be doing here. I'm on holidays and didn't properly read your initial post before replying but Dan is 100% correct.
There's a lot of things in PSAppDeployToolkit that are there to empower packagers, but I'd consider running any user deployment from the SYSTEM account as abusive. The Start-ADTProcessAsUser function is there more for simple requirements like restarting explorer or running some small amount of code as the user in support of a SYSTEM-based deployment. It's worth mentioning that in multi-user environments such as terminal servers, it'll just apply to one single user and the user that gets nominated may not necessarily be the user that you think it'll be.
You're not the only one doing this, so don't worry. There's many out there that feel like they're deploying in some kind of superior way by deploying user apps from the SYSTEM account, etc. All they're really doing is limiting the toolkit because giving more power towards esoteric but legitimate ways to start processes changes from being handy to being dangerous in the wrong hands, therefore we just won't implement them.