From the problems you've described I'd start with new shift cables and cable housings. Ultegra derailleurs will last many many years, cables and especially cable housings can go bad in a matter of months, especially when ridden in rain or dust. Replacing them is not such a tough job, cut the new housings the same length as the old, the rest of the job is simple and intuitive.
And hose out the inside of the shifters with WD40.

Al