Remove negative slopes from signal
I would not do slope detection, I have spend a lot of time solving a similar problem and slope detection didn't work for me. 

I have a few suggestions:


Do a moving average, this would act as a filter and smooth the signal. Especially, your signal is slow, so you can oversample and easily do a moving average. Realize, this will shift your peaks.
If you must get the peaks in precision, do a BPF, this would take out all HF noise and DC. 
Assuming you are measuring lung capacity, seek out the peak and dip points and subtract 
them to find out the magnitude, don't assume a bias and try to calculate from there. It sounds like you have a virtual zero point and your try to see how much the amplitude of the signal. You can divide the result by two to get what you want. 


You can do BPF and last together and you can get a clean measurement out of it.