A heat diffuser, sometimes called a flame tamer, might help. They make them for gas, electric and induction ranges.
I find when I'm making something like a large batch of soup or stock, I can't get my gas range down low enough to produce a light simmer unless I use a diffuser. If I put it on simmer, that's too low, and while there's some ability to adjust it in between simmer and low, it has a tendency to down to simmer, so I use a diffuser and then low works. I have two different types, sometimes I need both.
I have a similar problem with the induction burner, but I don't have a diffuser for it yet. Newer standalone induction burners have more temperature settings, but I don't think they make ones that have continuous adjustments, at least not for the home market.