Perhaps as a community we could do like an “upgrade barn raising” where the more tech savvy folks (the audience of WP Tavern) could volunteer a little bit of time every day to help get folks set up correctly on the latest version, like install4free used to work for installations.

I can't see how that could help. Upgrading is literally just a matter of clicking a single button, so there's not really anything to help with. The problems would be related to testing plugins, themes etc. which the site owner would need to do themselves since they know how their own site ticks better than anyone else.

Maybe there are exceptions where some technical help could be needed, but those would be fairly few and far between I imagine.