Figured it out. It was the item frames I had marking the chests. I thought it was the Redstone updates (hopper clocks...yeah...) but when I broke the frames the game started responding on my phones again...
I understand item frames, being entities, are causes of lag in mcpc also. Work on that, will ya Mojang?
Confirmed on a new kindle fire 7", LG G2 and LG Sunset (l33l). Survival Multiplayer with a smokin' fast laptop running the win10 version as LAN host.
I have a fairly large redstone testing world with a lot of mechanisms and auto farm designs, but putting up a map wall in the SMP base about kills the game - can move around just fine but destroyed blocks sometimes take several minutes to drop their respective items, mobs ignore you unless you stand still for about the same amount of time it takes for items to drop. I've danced with a creeper for about 10 minutes until it detected that I stood still for 2 minutes and therefore exploded at that location when I was about a chunk away. (comical to see these dudes spontaneously 'splode though lol).
I cleared up the lag by taking down all redstone stuff, the maps on item frames, a comparator-clock fed trash bin which drops items into lava, enchanting table and anvil.