Sorry to hear Gizzy's still spraying....unfortunately, I think he's an incorrigible sprayer and feels the need to keep marking, and it's become a ingrained habit with him. I think I would get a bunch of cheap towels, fold them so they're thick and pin them on his bed, to make it easier for you to manage, rather than having to wash his bed. Are you using scented laundry detergent and/or dryer sheets? It's possible he doesn't like the scent, so I would wash the towels in unscented detergent.
I do hope you will soon be able to move into a house to have some sort of outdoor enclosure for him.
"We humans are indeed fortunate if we happen to be chosen to be owned by a cat." -- Anonymous