It looks like you've got a pretty good system already! We tried to think of any stories we've heard from other harp owners about this type of situation, but nothing is coming to mind. It seems surprising, but I guess this doesn't get talked about all that much!
You're already doing the two things we think of as the most important - keeping the harp in a corner so it won't get knocked over, and keeping it on a hard floor so it's more stable if it does get bumped. The fireplace grate seems like a good addition, although I sympathize with the difficulty of moving it when you want to play your harp.
If you do build a cabinet, I doubt you'd need to worry about temperature, but it's possible that your outside room humidification efforts might not penetrate into the cabinet. The only way to really know is to keep a hygrometer in there so you can monitor the humidity. There are inexpensive little digital hygrometers that will let you know if you need to humidify inside the cabinet as well, or will give you some peace of mind if you don't need to.