In St Regis the trail does not start until Little Joe Creek Road for the Route of the Olympian. When you say the route east of Tarkiro - I think you are referring to Tekoa, and that detour is well documented, as well as the one around the private land with the missing trestle. There are a lot of good video "vlogs" out on YouTube of people biking these sections and I found a trail journal of someone who recently hiked it. Plus, there is horse and wagon group that does and annual trail ride end to end of the Palouse to Cascades Trail and posts a booklet (free to download) with updated trail and detour information. There are locked gates in some areas, but if you register with the state they provide you with combinations to the gates.
The area with the closed tunnel on the east side of Tekoa has a large rockslide on the west side of the tunnel and the trestle is missing a lot of decking and, in my opinion, unsafe. There are plans to re-deck the trestle but we are planning the detour unless we see evidence that the dangers have been resolved.
I have probably spent around 20 to 30 hours reviewing aerial maps, trip reports, and videos, and the route looks very doable once you plan for the detours. Another factor in the section west of the Columbia River is tumbleweeds up to 10 feet deep blowing into some cuts and tunnel entrances. The wagon riders clear those before their ride on Memorial Day but we are coming later, so planning a road bypass of this area.