I have had lime stone in my system before.. It makes the PH uncontrollable.
Your welcome to try it if you want, personally I will stick with the calcium carbonate. The inconvenience of having to add the calcium carbonate once a month is not worth the hassle of constant water replacements trying to use lime.

I have used powdered lime before and the limestone. Neither worked for me..

It's been my experience that limestone dissolves at a faster rate than calcium carbonate. I certainly don't claim to be all knowing on this subject, I can only tell you what I have observed through years of trial and error.

If you think one will be better than the other, then do the vinegar test, or something similar, on samples of each. That way you can make your own conclusions through your own experimentation..