Encumber should apply...? Move boosts don't apply because the ally isn't 'playing a Move card' I think.
While I'm not opposed to the current functionality (which seems reasonably balanced), that does seem odd, just from a thematic/conceptual viewpoint. Team pushes are considered some sort of weird 'encouraging them to exceed their limits and give just an extra push', so their weird interactions make a sort of 'heroic effort' sense. Team moves indicate basic commands being given, so you'd think if the person can move on their own, they could apply their own bonuses as well. Of course, that's negated by the fact that the move isn't adjusted by racial movement bonuses (or penalties) either.. In any case, Team Walk is more of a coordinated tactic than it is a command, so it specifically doesn't break any thematic components in being as it currently is. Moreso, it's already a darn good card, it doesn't need any extra boosts. That's my take
