I have Travertine which is a type of limestone, one of the harder ones but it is limestone. What kind of limestone do you have? Leuder stone is softer and then there is also field stone limestone and cut quarry blocks. If you have the cut blocks then you have a problem no matter what kind of water you have because that chalky stuff will wash away, get mildew stains, leech impurities into the pool and stain, etc. I will assume you have Leuder.
See this post I made earlier, It is more about the CSI of the water not the salt. We did not treat our travertine. All I do is wash it down if we have a big party to get some of the residual salts off the coping. I spray it down at least once a month, sometimes more.
Keeping the balance with Salt water is not too hard. Getting TA down and CH up is the only part that was hard at first then they stabilize. Salt Water will tend to go scaling more often than etching. Just watch your acid applications and maybe dilute the acid before adding it. I have not but I usually put on the waterfall and it keeps any acid from splashing back on the tile/coping.
A few tips: Use liquid chlorine for shock instead of Cal-Hpochlor, once you have everything stable test for chlorine and pH about twice a week, TA about once a week and CYA and CH about once a month.