I see cars on 98 momentarily drift into the bike lane all the time. I conclude that nobody should ever bike on 98 regardless of his right to do so. It's a bad idea. The bad drivers win.
I briefly rode my bike in the bike lanes of Hwy 98. I got off of 98 as fast as I could and I found the experience thoroughly unnerving to do again.
With the right-of-way that 98 has it seems like they could put in a small path 15-20 feet off of the traffic lanes without much issue. It wouldn't have to be wide or paved. They could just use crushed gravel.