I decided to attempt Barry Point following the Annular Eclipse of 2023. I approached it from the South and drove clockwise to a point north of the peak where a dirt road heads South East up the hill, parking at 42.113809, -120.793403.
This last leg of the drive contained pretty deep ruts (presumably from people driving through the snow), a few mud puddles (even in October). Definitely need high-clearance and probably 4wd once you leave the gravel road and turn SE.