This is a very simple matter of layers and masking. Are you familiar with those?
I can do it for you if you don't want to do it yourself. It's what I do.
Yes, I think you should add a Solid Color layer of light grey (roughly an average of the blanket colour) and mask it onto the blanket, then lower its opacity.
We'll talk more about the cast once you've finished the Channel Mixer class.
Regarding the blanket and tub .... I understand why you'd like to get rid of the tub, but what's wrong with the blanket?
This happens to all of us from time to time. Nobody knows why.
You'll just need to re-load your actions. I agree it's a hassle.
To be safe, can you do this for me?