Yes, I always have slightly damp skin when applying any moisturizers.
I've been plagued by dry skin my whole life, so I feel your pain. Everyone is different, but the few things you mentioned are a no no for my dry skin. One is hyaluronic acid, makes me look dehydrated and sickly lol, and the second is putting moisturizer on damp skin. Water if allowed to dry on your skin actually causes more dryness, and when it mixes with moisturizer it just dilutes it. Masks never helped me, made things worse a few times.
Cleanser I swear by Juice Beauty facial cleanser (the Green Apple one)
As for moisturizer/dry/anti aging skin, Algenist is very good for the face, body I like Pericone. Dry patches on the face can be gently scrubbed away once a week, no need to do your body.
A hydrating foundation, I like Juice Beauty serum foundation applied over moisturizer so you have double moisture. Juice also makes some very good moisturizers.
Stay away from drugstore brands, they are lousy.
One other thing is a humidifier, have one in every room, or at least your bedroom