Why a lot of batts are covered these days, they lose a lot of punch in cold due to internal resistance going up.
In older days batts had a problem with being on cold floors and it discharging them, or at least sped up the natural losses, modern plastics cured this though. So from that point of view you can leave it on concrete indefinitely. With that said the reason I still do it is purely trying to keep cold at bay from it while in storage as the lower the internal resistance the better the battery is.
If you keep it trickled up every few weeks, even on cold floor, it will be fine though.
If you absolutely had to keep it fresh then the panel above would help keep it where you left it I'd think. As Alan has said, your looking at small numbers here so I personally dont think it is worth it.....to each their own though
P.s some good info here on the older tech our batts use....not long till lithium is the norm though thankfully.