It's not a problem to shoot into the concrete after about 24 hours. In fact, it's much easier while the concrete is still green.
You don't need to do anything special to cure it in a basement. That's only an issue if you're outdoors where the sun or wind could dry the surface faster. Like you mentioned, it's better not to use a curing compound so you avoid issues with flooring later.
I wouldn't bother with an accelerator either. It'll just make the finishing job more stressful if the concrete sets up too fast. Just pour and finish it tonight, and you'll be good to go tomorrow night.
By the way, concrete reaches it's design strength in 28 days, but continues to cure and get stronger and harder for 50-100 years.
