Actually in Northern Michigan they are exploring several mines for pumped hydro storage Most of the mines up there are tapped out and they virtually all have water at the bottom and lakes or area that could be lakes at the surface. Much of the problem there is just how far it is they will need to run power lines to be able to leverage the facilities efficiently. Big cities in the U.P. simply don't exist and for that matter neither do vast solar farms :-)
Certainly if you have significant height difference as well as lots of water then investigating pumped hydro storage should be on the list.
You are correct that containers only appear to stack neatly on their own but require manually installed twist lock connectors to stack, well as least as I'm aware they are still manually installed. This is why I wouldn't think stacking them would be desired. Best is to keep them all on a level surface both on the surface and in the mine. The process of grasping and releasing them from the top though is well automated and reliable.
I am aware of the huge CO2 impact of making concrete. Yes it seems like the blocks used by the tower could be lower quality less dense concrete and while I'm no engineer it seems that if you stack them high enough the ones at the bottom will need to support all those stacked above and that won't be trivial. In my theoretical container there is only a prestressed concrete piece laid in the bottom of the container to support the rocks and sand that fill the remainder.
You say I'm trying to make it more complicated than the stacking tower but that thing has a lot of moving parts and needs to do everything right or the entire stack could be in danger. Automated elevators ('lifts' technically) have been around forever. I worked on construction of one myself more than 40 years ago. I built the controls for the thing and back then they were relays, limit switches, motor controllers, big fuses, a couple switches and indictor lights, one big red Emergency Stop button and a few PLCs. Today my golf watch probably has sufficient computational power to run the entire system.
Additionally where do all those stackable blocks come from? I'm not talking about manufacture but where are they when they aren't in the stack? Seems they'd need to be within reach of the tower, which limits the number available to the surface area under its reach. If they have to be brought in from outside that reach, then that adds complication to that solution as well. Further, the lower levels of those blocks store a fraction of the energy of those nearer the top. Your suggestion to put the thing on top of a cliff would greatly improve the efficiency given the height of the cliff multiplies the amount of potential energy storage.
Finally I'm not stuck with a requirement to use actual shipping containers. If their value has gone way up then come up with something else. At one point I knew of thousands of them stacked in yards and nobody wanted them. It was too expensive to ship them back to Asia to refill them, but that's some time ago. Using the lift method the shape of the containers is perfect because there is little space between them when stored either on the top or bottom of the lift. Other dense rectangles with lift attachment points would also function admirably.