I think you've got it right here and I hope this gets seen. US Border Patrol denied my entry to the US once because a coworker and I were coming over to overse

I think you've got it right here and I hope this gets seen. US Border Patrol denied my entry to the US once because a coworker and I were coming over to oversee the installation of a number of electrical devices our company built/designed/tested and shipped to the client. We didn't have the adequate paperwork to state that this was a contractual "job" and we were simply there to assist local tradespeople in the installation should they have any questions since, you know, we designed the thing. When we were turned around at the border it was explained: without the paperwork to detail what we were doing, that this was agreed upon ahead of time and likely a bunch of other legal matters they had no method of knowing whether we were hired to save wages that would otherwise go to an American citizen. We weren't being paid for this work, it couldn't be done by anyone else (short of them taking the design work and learning it from the ground up over several months) and we were still denied entry. OP, work, even if free, is still work. Contact legal aid for what you are and are not allowed to do.