As we suspected, we were doing a few things wrong:
This is from the 3d edition rules, available online as a pdf.
LEADERLESS ACTIVATION:
3.11 Individual Units and Stacks.
An individual unit may activate with or without the assistance of a leader. An individual stack (everything that’s stacked together in one hex) may also activate with or without the assistance of a leader, no matter what types of units are in the stack. Units that activate without leaders can’t move closer to enemy units that can harm them with Direct or AT fire (5.4).
This also resolves our question about how to load a gun on a transport with no leader present. As long as the transport and unit to be transported start in the same hex, they're good to go.
TRANSPORTS:
5.31 Harmless Enemies.
A unit may freely enter and exit hexes containing only enemy leaders (see 6.71 for possible leader casualties) and/or unarmed, empty enemy trucks, wagons or sledges. Such enemy transports are eliminated if the moving unit is a combat unit. Unarmed, empty transports can freely enter hexes containing only enemy unarmed, empty transports. They have no effect on each other
...so my wagons were doomed.
There's probably some other stuff too. I'll give the rules a thorough re-read between now and our next meeting.