Minecraft Java Edition – Can Mobs Spawn on Slabs and How to Prevent It?

Mobs don't spawn on glass, ice, half-slabs, and stairs. Your loft should be safe as per the minecraft wiki.

Spiders can climb glass walls, so you may want to add a small overhang or a row of ladders if there's an entrance.

There are two points to remember that may seem contradictory: first, like Nicholas pointed out, you need to makes sure that your mobspawner is the only nonlit space in a pretty big area around you (I think the area's actually about 150x150 blocks), but second, you need a lot of empty space around. In other words, minecraft will choose places that have a lot of surface area (not volume) to spawn mobs in, so if you were to have a lot of open caves beneath your mobspawner, the game will flag that area as more likely to spawn mobs in. You just also have to make sure that it's all well-lit, then you've effectively tricked the game into flagging that area to spawn mobs in, but then conveniently your mobspawner is the only dark area where it can do so.

I would recommend you take a look at this tutorial. You may not want that particular style of mobspawner, but it goes over the prerequisites of any good mobspawner quite nicely.