I'm trying to transfer units from my wagon and builder to my town next to them (which has the inventory space), but all it gives me is a failure to transmit resources. I can transfer them between the two machines with no problem, but can't transfer them into the town.

I do not know the answer to this but I will give a guess...

A wagon can not transfer troops to a hero that has no troops. The hero must have at least 1 of that troop first to be able to receive more from the wagon.

Perhaps it is the same when transferring troops to a city. If the city does not have at least 1 of that troop in its inventory already it may not be possible.

As I say, this is just a guess!

You can't transfer troops to a freshly established castle for 2 weeks.

I learn something new every day