This seems to be a pattern with Gizzy, if you're out for a fair amount of time that he gets anxious and sprays.
As far as a house, there are all kinds of outdoor enclosure one could use. Some even attach to windows. I think I would wait and see how he behaves. Just being in a bigger space with more rooms may solve his spraying problem. Certainly hope so, as I think you've tried everything.
"We humans are indeed fortunate if we happen to be chosen to be owned by a cat." -- Anonymous