--edit -- AJ beat me to it - and is more succinct!
Skip the DI stage and just go with RO... you need some ions in the water after all, no point in paying extra to strip absolutely everything out - and then add some back in. Since you have a softener, you can pass that feed into the RO media - will help preserve the filters long term. The primer is the perfect guide for this... or you can use Bru'n water for a more advanced approach.
Is it best to just get an RODI system to clear out that Sodium and Chloride?
RO is how I decided to manage my terrible water profile - because of very high sodium and bicarbonates. It works well - and I have been very happy with the results in my beer. You can also purchase RO water at the grocery - and that is probably a good idea to brew with - before you spend the money on the filter. It adds some complexity to brewing preparation... however, IMO, is worth the improved results. It may take a few brews to dial in your additions, and get past an nerves about adding stuff to the beer.
Would RODI water help bring down my total Alkalinity too?
Yes, and you are starting from a blank slate. Expect RO water pH to be between 6 and 7, varied by the efficiency of the media. Mine runs about 6.4 from the filters, with minimal alkalinity. This will allow you to brew fairly pale beers, but may require some alkaline additions (baking soda or better yet, pickling lime) for darker beers. I would suggest a good calibrated pH meter to help manage this. You can follow the advice in the Primer as a starting point or get a lot more involved (managing pH and managing flavor). Bru'n Water spreadsheet can help you to make good choices on additions and process. Without salts in the brewing liquor the beer is likely to be terribly boring.
Are there any concerns/benefits with using RODI water?
I don't suggest drinking it straight, and there are some health concerns if you drank a lot of it over an extended period of time, I prefer water with a little hardness for drinking. Coffee and tea made from RO is pretty lifeless.
It is the perfect blank slate for brewing however, with some salts added. Also consider, the RO is fairly corrosive, so make sure to plum with PEX and not copper or brass past the filter. Small filters work well, but require some time to collect enough liquor to brew with... I have (4) 5 gallon spring water jugs and store my RO in those with foil lids - preparing a day or two in advance.
So to sum up:
A) The simplest approach is to brew with the Primer recommendations and adjust your additions from there with the next batch. I would start here before any big spends and use store bought RO for a couple of brew days.
B) A more complex (and perhaps satisfying) approach is to invest in a good pH meter, RO filters, and learn to manipulate both flavor contributions and mash/boil pH based on your recipe with mineral additions. Reading the new "Water" book and using a spreadsheet like Bru'n can be very instructive.