First, if you are not a fish, you are most likely drinking water that is softened, and no...it tastes MUCH better than unsoftened water. The softener usually uses salt pellets to collect as much minerals as it can. This is why if you leave for a week, your water is not rusty or yellowish because of those minerals in the water. This is usually something reserved for people who use a well (well, they benifit the most from it) since city water is highly treated water, mostly to ensure its safe to drink, but also to help soften it out.
As for my fish, I was in a similar situation because I was moving from a house without a water softener into one that used one. I was basically forced to take most of the water from the tank, and the rest from the old house, and transport it to the new place. Here is what I found out....
It is EXPENSIVE and WASTEFUL to soften water that goes to outdoor hoses, toilets, or heating systems that use water (not water heaters, heaters that use water, like in the olden days). So, you can get unsoftened water from your outdoor hose hookups, unless you are completely rich and can afford to buy salt pellets every other day and enjoy the excersize you get from taking them all downstairs. Outdoor plants generally DO NOT thrive in softened water since they need the minerals, so if you are that rich to soften your water that use water the grass with, you most likely have a crappy looking lawn or fertilize every week.
Ok, just wanted to dispell those myths. I want to make a big smart comment about the softened water tastes bad thing, but I wont.
I think you may have a couple of choices with your tank. you can use the softened water and add buffers to get to the right Ph and general hardness your green terror desires, or you can test the water that comes out of your outdoor hose to see if that is the same as your water before the water softener was installed (just to make sure it is not collecting more minerals because they are usually fed with pipes that could be older or made of other metals, which water does pick up over time).
I have also heard of many people keeping cichlids in water that is not buffered nor at the desired Ph or hardness (I do this in one of my tanks with yellow labs, because they are used to that type of water). This is where I would not be the expert, but you may, in small amounts, start aclimating your fish to softened water, very, very, very slowly and it could do fine. For my yellow lab tank, I just use the water out of my sink, that I drink from, and carries city water, and they are thriving because it is the only type of water they ever lived in.
One more thing, in my opinion, I would be leery about doing such big water changes every four to five days in your tank. I am assuming that it is well established and you could be depleating your tank of bacteria that you need to quickly for it to replace itself. If your tank is not well established, which I dont think is the case but just wanted to add it for other's benifits, you could be creating a situation in which you are keeping your tank is a constant, never ending, cycle in which you are only keeping your fish healthy because you are taking enough ammonia, nitrates, and nitrites out every four to five days to keep them at a less than lethal amounts. If it was my tank, I would do about 15 to 25% water changes once a week (7 days) so that the tank invisible ecosystem can survive and thrive. This is an instance of 'too much of a good thing can really be bad", in my opinion.
Lastly, I appologize if I sound judgemental or degrading, but I have done a lot of work on houses, both indoors and outdoors, and know a little bit about water softening. I also know from my experiences in this hobby a thing or two about fish, but not everything and I have never kept a green terror, so I am not the expert on them at all. I just wanted to help you get good information. In the US, where I live, nearly everyone who does not live in the bigger cities, uses well water (straight from out of the ground) that is almost always run through a water softener before they drink, cook, or bathe with it.
