I just leave my resin items somewhere in the kitchen (on the table or stove) where I know they will not be disturbed for a long period of time.
I haven't ever covered my resin projects while they were drying, and I'm wondering if that may be an issue with your projects. I would think that the item would need air circulation around it in order to dry well.
I don't remember the name of the resin I use, but it's the measure/pour/mix/use type. Although, I have recently purchased Mod-Podge's 'Dimensional Magic' (eight bucks for a small bottle) and it works just like resin, but without all the setup and nonsense.