Here's how I'd do it. Go ahead and feed your RO/DI from your water softener. I asked Russ at Buckeye about this, and he said absolutely.
Run your RO/DI to your brute. Put a float switch in it. ONLY fill your brute up as needed - turn your RO/DI on and off manually, when the trash can gets low. You want to avoid cycling your RO/DI, as the membrane "leaks" between cycles. The float switch is a safeguard, so that when you turn your RO/DI on, and forget to turn it off, your brute doesn't overflow.
From your brute, you will need to pump to an automatic top off in your sump. Make SURE you buy a unit with a backup - so that if a float switch fails (which it will), you don't overflow your sump/tank. Also make sure that your feed to your sump is higher than the top of your brute - otherwise, once you start the pump you will be starting a siphon! I take the output of my topoff and put it into a much larger piece of PVC that goes into the sump - that way it feeds above the storage unit, but trickles down the PVC into the sump, and when the pump quits, the flow quits.
Bill
215g FOWLR... and anemones, GSP, gorgonians... carp, that isn't FO!
"I killed my first SW Fish in 1971..."