GG1man: I don't have any experience with Lionel electronics; I'm strictly DCS. But your analysis is correct. Problem with the wifi is that there still some rough edges in the firmware and the app, so it's difficult to tell whether they or the operator are to blame. Just as layouts differ electronically, now there is introduced the vagaries of networking.
Chreyl, I am using 2 Samsung Galaxy Sprint phones, an SIII & an S6, and a Samsung wifi Note 10.1 tablet. Are you using the MTH or home setting on the wifi unit? You really have to be working at the layout where you want to run well.
If you're using MTH, I still lean towards your Galxy jumping to another network. If so, to get the wifiday demo working, I'd say try deleting that other network from the list of wifi netweoks under settings/wifi, and unchecking any "connect automativcally" boxed for networks other than MTH.