Is it possible to drive from the Huon Valley to Mt Field, Franklin-Gordon, etc without going through Hobart?

I was in the Huon Valley last week (where we're considering moving) and was contemplating a stop at Mt Field NP on the way back to Launnie. Google Maps was playing up in strange ways.

Directions from Lonnavale to Mt Field Visitor Centre: only shows a trip through Hobart, approx 2 hours.

Directions from Blackwood Farm (a site right next to Lonnavale) to Mt Field Visitor Centre: shows a much more direct trip, half the distance, and approx 1.5 hours. Google Maps warns that this trip (clearly through country roads) may have private/restricted roads.

I was wondering if anyone had personal experience efficiently getting around Southern Tas. Don't like Hobart traffic much.

Imgur link: https://imgur.com/a/WpVyEZl