I'd just do a sediment filter and two carbon filters, should be good enough for your needs depending on source water quality. The extra sediment filters will do nothing unless you stagger micron sizes from high to low (night let you go longer between changes), but that would still end up costing you more. Sediment filters are cheap tho, but still I'd just run a single 1 micron filter on the front end and change it when your output drops significantly.

As for carbon filters, two I probably overkill but if you have the stages for it anyway it's just insurance. You can run 0.5 micron carbon blocks if you want but you would probably have to change them before the carbon is exhausted.

All of my RO/DI system's waste water travels 50' to a 55gal plastic drum in the laundry room. I coordinate washing clothes around when it runs so very little is ever actually wasted. There is an emergency overflow drain on the drum so that it doesn't overflow onto the floor if it gets too full.

An RO membrane is cheap why not just run a regular unit and skip the resin? I would imagine it's the membrane itself doing most of the work and a high rejection rate one is still reasonably priced and last a few years if you take care of it.

out of curiosity how does this work? normally you're feeding water under pressure to the machine and I'm guessing a solenoid in the machine opens and closes. is the barrel elevated to gravity feed into it instead?

So what happens when there's a flood? What happens when the city has to swap to chloramine due to E. coli outbreaks? Etc...

That's the reason I use RO. It's insurance for when the normally good tap water isn't.

The water barrel isn't tied into the washing machine's plumbing, I just turn off the cold water tap and manually fill it from the barrel with a Danner Mag Drive pump which has a hose on its output. When the water level in the washing machine reaches the right hight the solenoid mechanism makes a 'click' noise, I unplug the pump and remove the hose. We have an old top load washing machine, if it was a new front load I don't think this method would work.

Agreed; there will always be a chance of tap water contamination (flushing of pipes, heavy chlorination, etc). I suppose in an event like that (like Winnipeg just had) you would A) hope you had enough freshwater stored to get you through or B) start boiling if you got desperate.

On a somewhat side note; but related. I'm also wondering about the merits of a UV sterilizer after the filtration; but before the salt mixing stage. I know this won't touch chlorination; but I'm curious what type of bacteria it would actually help not introduce into the tank (if any). I, personally, don't want to put the UV sterilizer into the tank as I'm a believer of keeping good bacteria around (please don't take offense if you use one; it's just my personal preference).