I have successfully treated water as low as 4.6 pH with downflow, backwashed AN filters. Upflow won't do that. You have to know the hardness in the raw water so to not 'cement' the mineral.
To do that the dealer has to know what they are doing. A backwashed AN filter is a top dome hole polyglass tank with a backwash only control valve on it. You can use any control valve brand and model as long as it is capable of servicing the size of the tank that has to be used and provide the proper backwash flow rate for the volume and type of mineral used. That volume depends on the pH of the raw water and the peak demand gpm of water used in the building. Very simple and dependable with very little maintenance. I sold one yesterday, calcite only not mixed bed, for a delivered price of $600. That was with a Clack WS1 control valve with by-pass valve.
In your case, there will be 6-10 gpg of hardness added to the water and you can add a softener at any time; just plan on its space requirement when you install the filter.
Without a retention tank, I seriously doubt you will get your feeder system to provide 7.0 pH very consistently. It will probably be all over the scale and on the high side. Too much soda ash usually causes a slimy/thick feel to the water, I don't know about lye; since BobNH suggested its use, he should.
You could use a static mixer (a special piece of plastic pipe with baffles etc. in it) but IMO (I've never done it) you'll probably have a real tough time getting the dose and mix strength set correctly without a retention tank. I suspect you already know that from many attempts at getting the thing to work. Soda ash will work fine for your 5.4 pH. All you have to do is get the mix strength and dose right and prevent the precipitation of soda ash out of solution in the bottom of the solution tank, and then not run it out of solution. And keep the injector and check valve (ceramic balls) clean so it/they open properly and on time.