I have suffered with dry skin since I was born, sadly, so know your pain! Baseline is as good a moisturiser as any, but there are a lot of other factors which make a difference ime. These are some tips I have picked up over the years... Hopefully some are helpful!
I think moisturisering frequently throughout the day can be as important as which moisturiser you put on. It sounds like your skin barrier might be impaired atm as your skin is having a hard job keeping it's moisture in - see "emollient therapy" as a way to fix. Not very easy to do though if you wear makeup.
Maybe let the Bassline soak in rather than wiping away if you have time? As I think wiping off moisturiser can be drying in some circumstances. Or use the Baseline at night, and something less greasy in the day, that you are happier to use. " The best moisturiser is the greasiest one you will actually wear" (eczema.org).
Have you looked into the other side too - drying factors? For example, what you are washing your face with? Maybe whatever you usually use is too harsh / drying for the moment?
Silky pillowcases can be helpful to prevent cotton sucking moisture from your skin (and hair) at night. You can get them made from silk or bamboo, but I have just sateen and they work well for me.
Hydration and diet can effect skin moisture too, if you haven't already thought of it. I did a low fat diet once, years ago, and looked like a lizard within a couple of weeks. Healthy full fats are the way to go ime.
Having hot baths or showers can be very drying to skin. Warm is better, with something called Oilatum or colloidal oats if possible. Make sure to moisturize within a few minutes of getting out of the bath or shower, as your skin is especially vulnerable to drying out then.
Depending on how bad it is, consider "wet wrapping" - probs fiddly to do on the face (I have never done it there), but extremely effective for basically forcing moisture into your skin.