Actually, what you descried is a 94% change. I'm not sure that I'd go that far either. While you're correct that if your tap and tank are similar in their chemistry that large changes aren't going to stress your fish in the water chemistry sense, low water level and the tighter living conditions can certainly be stressful, think if it like the ceiling slowly coming down on you.
Two back to back 50% changes will provide you with a 75% water change without a stressfully low water level. Also remember that since your tap has about 5ppm NO3 that a 50% change won't result in a NO3 level lowered by 50%, but by (previous level/2)+5ppm
As previously mentioned, clean out your filter, rinse media in old tank water, and clean up anything that would provide a source of decaying matter.