Hi mate,
Firstly, i have no experience with cystic fibrosis and I know little about it, so I have no advice on that front, but I do know about depression and medication for depressive illness. It does sound like you are suffering depressions whether they are caused by medication or not. Your physical health problems are certainly not helping you.
In my opinion it sounds like you should be on an anti depressant to help combat your low mood. It sounds very promising that you responded to mirtazapine but it is unfortunate that you are experiencing solmnolence. The only time I have heard of mirtazapine causing slurred speech was in a case of serotonin syndrome induced by the medication, but I am not a medical doctor. Do you know of any other reasons why you may be experiencing slurred speech?
In terms of solmnolence, mirtazapine is considered to have its greatest sedative effect at about 7.5 mg (if I remember correctly) so increasing the dose should not make you feel more sedated. However, I have heard of people complaining that increasing the dose made them feel tired all day and I had a similar experience myself (although I am not sure if it was caused by my depression). The fact that you are finding it difficult to sleep at night suggests that perhaps you are depressed, although you claim to not be experiencing low mood. Perhaps it may be caused by some of your other medications, I do not know.
Are there reasons other than unwanted side affects, that make you wan't to stop antidepressant medication? Would you consider taking another kind of anti depressant medication?
Best wishes,
Steve