Im fairly new to RIU, but I do have a lot of experience in water quality so maybe I can help on this one.
DO NOT USE THE SOFTENED WATER!. The added sodium will screw everything up. You are better off using tap water than softened. If your tap water is more than 15 to 20 grains hardness then use General Hydro nutes specified for hard water. However you said you have an RO? The limited tank capacity of RO (2.2 Gallon) can be a problem but the AG only uses 1 gallon (you didnt say you had an aerogarden but Im assuming cause this is in the aerogarden section). Plus you can add a second storage tank to the unit for like $50 and double the capacity to 4.5 gallons (this is what I did). You can also simply empty the resevoir to a pitcher, put in the fridge and wait for the RO to refill, increasing storage.
DO NOT TRY TO REUSE NUTE WATER! You cant filter out TDS (salts) with a "rigged" filter.
How many gallons do you need at a time is a good question? Did I read 55? This is an Aerogarden thread so you may be confused.
If I were you, I would reconsider the 55 gallon res and got to a 22 or less. 55 gallon DWC sounds nice at first, but thats a lot of nutes to add when doing by weekly res changes, not to mention a pain in the ass to empty, as it will weigh a couple hundred pounds! I was going to do that and chose to go with 4 - 10 gallon containers instead. Much more manageable.
I have a softener and an RO and only use the RO water in my AG. Also RO will lower the ph a little as well. Beware of calcium deficiency when using RO or distilled water as it has no calcium or magnesium, so make sure your nutes have some cal/mag or buy some botanicare cal mag and add it.
Also, regarding rigging a filter to the AG to remove the softener salt, nearly impossible. The micron size that sodium dissolves to is so small, only RO and distillation will remove it. Thats the main reason RO's are frequently sold with softeners, to remove sodium. A carbon filter wont touch it.
Also, the softener does not run the water through salt crystals to soften the water. It runs it through a tank of resin that exchanges positive ions (calcium and magnesium) for negative ones (sodium). The salt is simply used to clean the resin bed. The salt tank is a brine drum to hold salt and dissolve it to a brine rinse (salt water) that will remove the trapped calcium when injected into the resin tank) That being said the water in the brine tank would be fatally toxic if you fed it to your plants(TDS 15,000 ppm). The softened water from your faucets are not nearly as bad, but will still have elevated levels of sodium which not good.
Hope this helps! Peace!