The rapid shallow breathing is often due to lung compliance rather than an infiltrative disease in the lungs. If there is fluid around the lungs (pleural effusion) then it could be tapped off easily and fairly non-invasively. This would have been seen on the x-rays. If this is due to cancer invading the lung tissue then you're left with doing more chemo- a rescue protocol although the prognosis becomes much worse when we're doing these rescue protocols. The one chemo drug I don't see on your list that works well for lymphoma is Doxorubicin (Adriamycin). Adriamycin is a bag of orange fluid if it helps any.
Another potential cause of the increased respiratory rate is a side effect of the Prednisone. It may be worth a shot to wean off the Pred or go down to every other day and see if that helps.
The coughing makes me think something is compressing the bronchi. This is most likely the tracheobronchial lymph nodes. There is not an easy way to diagnose this as x-rays are not all that sensitive to visualizing lymph nodes in the chest. Again, we're left with higher doses of chemo as our only real option.
I know you don't want to hear it, but it may be getting close to time to make that hard decision. It is usually when we get respiratory involvement that we start thinking euthanasia. I'd still give Adriamycin a shot if it has not been done already- I suspect it may have been given the sick sinus syndrome as it can be cardio toxic
when we reach high cumulative doses. If not, then try that one and see if it helps.
Cough suppressants are another option to control the signs. Hycodan would be my first choice. Torb (Butorphanol) is another option.
I hope this helps, let me know if you have any other questions.