Greasy or tacky is fine at the start. That's just the yeast getting started. After that you should see it bloom in a couple of days. Too wet is when the it looks shiny from whey sitting on the cheese. Once the cheese blooms, the rind will dry by itself. It's not so much that the cheese is losing moisture (it's really not -- I've measured once or twice and only seen a few grams of difference in the first week or so). It's more the humidity around the cheese. Once the mold blooms, it will consume water.
When you say that you are using a morge, what are you putting in it? A morge is brine where you add mold/bacteria to wash or spray onto your cheese. If you aren't adding anything, then it's just a brine. For washed rind cheeses, you can make a morge by starting with brine and washing existing cheeses. The bacteria will end up in the brine, making a morge. Are you using another bloomy rind cheese to start you off? I would not use a morge on a bloomy rind, personally. Instead, just scrape some of the mold off of an existing cheese into your milk. But, if you didn't do that, then making a morge and spraying it on should work OK. I think you only need to spray it once (but I've never done it).