Still a little confused on the difference between -taH and -lI'. What exactly would the difference be between SID HaqlI' Qel and SID HaqtaH Qel ? Would the first be something more along the lines of "The doctor is performing surgery on the patient (in order to save their life / etc.)"?
-taH has a flavor of an ongoing action that might eventually come to an end but doesn't seem to have a set end time and might go on for some time. I suppose SID HaqtaH Qel might a good way to describe a major trauma case where the surgeon keeps finding more and more problems that need to be fixed and it seems that the surgery will never be finished.
-lI' implies that there is a definite and known finishing point and that progress is being made towards that finishing point. Most surgeries are planned very carefully and are more appropriately described as SID HaqlI' Qel.