I just did the popcorn ceiling in our den as a test for DIY (had the kitchen and FR done as part of a total kitchen gut) and it was surprisingly easy, but tiring on the arms. The popcorn came down really easily, but I spent the next few evenings after work touching up holes with joint compound and sanding. It was definitely worth it in the end and even though we didn't do crown, I imagine doing crown over the popcorn might be tough or not look as good due to gaps. Maddielee's suggestion to remove the area just by the crown might be a nice compromise, but I say - go for it.

Just a funny story about my late DMIL....She always kept cookies in a tupperware container in the oven...Well, you guessed it, one day, the oven got turned on and the tupperware melted...Not telling anyone, she put this melted "thing" out on her back porch and asked everyone what they thought it was.....No one guessed it was at one time a container full of cookies....It really looked like a piece of art...We've often talked about Gram and her taste in art.....

On my back, no. But I used to fairly often wake up with my sheets and pillowcase streaked with blood and mysterious injuries in random places. It took me months to figure out that the cause was my engagement ring. At the time, I had a marquis stone and would wear it to bed. I'm an active sleeper, so what was happening was that I was moving around and adjusting the covers, which was causing the stone to move to the palm side of my hand. So any time I moved anything with my hands, I was digging the ring into my skin. The only way I realized what was happening was when my husband grabbed my hand one afternoon, kind of twisted to hold hands with me, and my ring ended up slicing his palm. I didn't realize it was that sharp, so the next time I had an injury, I inspected my ring and found blood. I have a different ring now, but I won't wear any sort of pronged ring to bed anymore. Anyway, just a thought!

I’m no pro, but I’m guessing removal of popcorn, retexturing to cover seams and paint would be cheaper than cladding with wood or panel plus moulding plus paint. Easy way to find out is to get some estimates. They are usually free. Once you know how much each option is, you can decide.