A better way to soften water?

I am looking for a better way to soften the water for my tanks. I'm currently stationed in central Missouri, where the tap water is so hard that it is for all intents and purposes liquid rock. I've been using peat filtration to soften my water by putting large quantities of very well rinsed natural peat moss into ladies panty hose and putting it into an AC110. This has given me very nice, soft water just like I desired and the coloration of all of my fish has benefited as a result of my doing so.

The problem to arise today is the surprising amount of detritus being caught in my filters and rotting. I've had a weird rise in nitrates recently and I haven't been able to figure out why. My pothos enjoyed it, but my fish and I did not. For the life of me I could not figure out what was causing this. It became apparent when my six-week filter servicing came due. The amount of gunk in the FX5 was unprecedented for me. After servicing my filters, my perimeters stabilized (though with hard water as I didn't replace the peat) and the fish seemed quite a bit happier.

Is there a relatively easy and cost effective DIY procedure that I could attempt in order to soften my liquid rock, or will the extreme hard water be something I'm forced to accept?

EDIT- Aside from purchasing a water softener or some other permanently installed appliance, as I currently live in a rental.

Thanks all

virgil2090 said:

Do you currently have any driftwood in the tank? try adding more maybe

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Ah, I hadn't even thought of that, thank you. I'm always on the lookout for nice chunks of driftwood but I'm having a surprisingly hard time finding any. The rivers around here tend to only produce whole trees as driftwood lol. I'll keep an eye out!