I’m no expert with concrete but an inch sounds a bit thin, normally you would use 50mm for a floor screed otherwise you risk it cracking. If the floor is just a bit rough and dusty you might be better off with self levelling compound. I’d try to do the floor on one go, perhaps hire a van for a weekend and store your stuff in there while the flooring dries. That’s another bonus for self levelling compound in that it would dry relatively quickly. Alternatively you could use an epoxy floor finish which would be dry even quicker at the expense of being more expensive I expect.