Its nearly impossible to dissolve 1:1 unless you cook it.
That said you can disolve 1:1.02 with aggitation then you will have 1g per 1ml minus a miniscule amount.
In Pharma trade the packages are sold with instructions. They also sometimes contain one or two grains of saffron to color the tincture and make it easier to portion out.
Instructions are to dissolve each gram in 1.05 ml then cook to evaporate that amount to get the correct solution.
For home use why not just dissolve 125 gram of KI in 132 ml of water. It will dissolve correctly and give you 0.95 gram per ml instead of 1..
I still say cook in a cheap enamel container while running current through the container. Negative ions will increase dramatically, to nearly homeopathic level.
Small cheap enamal pots are about $4, break the lip on opposite sides to reach the metal and attach a 9v battery via clips...store with a magnet or in a lead lined container to keep the negative ions.