I’m not sure what you could use for gaps with the linoleum… Is it between the squares? You could try a silicone sealant perhaps but make sure it’s well cured before putting base and shelf back into the condo.
I’d use wire or metal clips that you pinch shut with pliers in the places where she can reach the zipties. You could probably leave most the other ties as they are. For the shelf edges, what about capping them with some safe wood like untreated pine. If you nailed a piece to the edges that was wider then the shelf thickness it would create a lip. So 1/2 inch or so would sit above the shelf surface. She could chew on that instead and not be able to get to the linoleum. It might not look great but when you have a chewer you sort of have to give in and provide them alternatives.
Edit to add: These images from rabbitcondo.com show some wood capping on the edges. It looks like these ones are directly on top of the shelf covering.

