So if I'm reading correctly, you have an elderly bun in his own room, and a baby on the way? Bun lives on hay and does well on this but you're worried about dust levels?
I'd say unless the baby is going to share the room, and Dennis is so active he stirs the dust up all the time, it really won't be a problem unless the baby happens to have a hay allergy.
I buy dust extracted hay made by NagBag, because I struggle terribly with hay even outdoors, but this is pretty tolerable, barely triggers even a tight chest unless I've been really shaking it up indoors. There are other makes of dustextracted. You could maybe use that for the bed, and fed his nice hay in a more controlled way to minimise dust?
The other alternative would be to use something like hemp bedding. Or - though this might not be suitable - I use straw pellets as a base floor. They need to be dampened to make them swell, but once in position as a good thick layer they compress and dry out quite quickly, and make a lovely dense flooring - with giants I want to ensure a soft floor to protect their hocks, but it gives a great grip and might even be easier to move around on than a hay bed. It's also incredibly easy to tidy up, once compacted it literally just needs a light sweep with a flat edge to gather any food, hay or poo. Being pure straw it is edible, but also not very appealing, so would be safe for a chewer.
As for toys, I have 2 great cubes from The Range that my guys absolutely love - just wire mesh cubes, but I stuff them with different forage mixs and they love chucking them around. There's some photos in my recent photo thread. Using bigger/longer forages takes more work, smaller particles fall through very quickly, ideally get a good balance between the two. Great with things like dried plantain, oat hay, shorter hays and readigrass.