I will try to contribute within my experience, I stand to be corrected when wrong (Which I am frequently).
I do NOT use continuous lighting because for me, it takes a *LOT* of light to get the desired effect (lighting) that I want.
I was a speedlight rookie for a long time, and until I spend some decent money and upgraded all my flashes (Godox Pro controller and 3 TT600 strobes, plus one that is TTL, I forget the model number), I struggled the get anything that was a keeper.
Then one day, after lots of Youtube University classes, I started to play with my stobes and it started to click. I got better real fast!
Anyway, some modeling lights to allow your camera to focus fast is all you need, with some decent strobes and I think you will have the results you want. Plus strobes (typically) are 5500K and thats more like the color your want.
Here is a doll baby I used to practice for a toddler shoot, all strobes, no color correction, "skin" tone of the doll matches what my eyes saw (98%).
Take a look at the EXIF, low ISO because my strobes are BRIGHT! And the quick discharge of a flash is gone before they squint... where as with ambient light that is really bright, all they do is squint (any model regardless of age).