small changes in LAB leading to huge changes in CMYK

[Justice23190311gwdt]

i work in a custom print shop that works with design firms which are very particular about their colors printing exactly how they think it should look. these colors are pretty much always PANTONE colors of some sort. to this end, when they request samples of color, i create a document that contains what the internet says the color mix of that particular color should be along with 120 variations of that color.

to achieve this while having the fewest amount of repeating colors, i often use more than one color mode setting when making a new swatch to get a wide variety of CMYK values. for example, after making some adjustments to its CMYK values ill switch the color mode to LAB and make a few adjustments from there. most of the time this works great as it changes the colors in a way i desire and doesn't stray too far from the original CMYK value i provided, but for some colors it makes massive changes to the CMYK color mix.

for example, when making variations of PMS Warm Gray 4C, i set the original CMYK value to "C 0, M 5, Y 9, K 29". then i make a new swatch using the mentioned CMYK value as a base, change the color mode in the new swatch menu to LAB and give the L slider an adjustment of +2. this small adjustment takes the color mix from 0, 5, 9, 22 to -> 23.69, 22.06, 25.96, 0. while the swatch appears to be similar in color on my screen display, the mix is completely wrong having undergone a massive change and this is a big problem when dealing a print product.

why does illustrator treat colors differently in this regard? some colors take the LAB adjustments just fine and don't stray too far, while colors like this have their mix undergo massive changes.

is there a way to change this so that making such small changes to different color modes doesn't completely throw off the CMYK color equivalent?

since when i use this method, it generally severely reduces the amount of black while upping the values of the other 3 colors by a large margin, i figured that there is a setting somewhere that handles how much black is used in a color calclulation but for the life of me i cannot find it or find the right phrase to google to find it. 

[Ton Frederiks]

What the Internet says about color conversion is mostly wrong, it does use simple formulas and does not use an color management with ICC profiles.

What you describe is the conversion from a 3 color component to a 4 color component space.

The amount of black generated is dependend on th CMYK profile used.

There are many possible CMYK values for the same Lab or RGB numbers, it de pends on the profile for the printing process.

[Justice23190311gwdt]

how would you solve this issue? what profile would you use to make sure that the color mix doesnt stray too far off of the original CMYK value when converting from a 3 component to 4 component space? is the issue just not solvable this way?