Turns out some machines in our network - mine included - have VirtualBox installed. VirtualBox creates a virtual network driver that was being used to broadcast the search packet (UDP, 255.255.255.255, port 14001) instead of the main network. For some reason, disconnecting my machine from the switch cascade made the problem to go away.
TL;DR version: if you have VirtualBox installed, disable the virtual network adapter before testing your multiplayer game in Unreal.