babipsylon:
everything should be mounted inside the pipe
I understand why you say that but I suspect that requirement will be a deal-breaker. As well as the limited volume the whole space will be very humid - just what you don't want where there are electric currents.
Even though the motor will only run a few minutes per hour (or even 1 minute per hour) it will consume a lot of energy relative to the capacity of any batteries that would fit into the pipe.
Have you measured how much force is needed to lift the sponge? That needs to be a very early part of the plan. Without knowing that choosing a motor and figuring out what size battery is appropriate will be just trial and error.
Another important issue IMHO is "equipment" to verify that the system is working. When you attend to it personally you subconsciously check that all is well and do things to ensure that it is.
I guess one way to ensure the system works is to make it significantly over powered so that it can't not work. But that has implications for battery life.
I must say I like @ChrisTenone's idea for something inflatable. Maybe you could run a small bore plastic tube from a pump inside the house out to the pipe. That would require only very little to be outside the pipe.
...R