A single word meaning “absolute control over something”

I'd suggest you reconsider stranglehold, which actually is nowhere near as mild as you think.

stranglehold

1. A grip around the neck of another person that can kill by asphyxiation if held for long enough.

2. Complete or overwhelming control: in France, supermarkets have less of a stranglehold on food supplies ODO

If you're still not happy with it, consider:

chokehold

1: a hold that involves strong choking pressure applied to the neck of another

2: absolute dominance or control : had a chokehold on the city's finances M-W

throttlehold

A vicious, strangling, or stultifying control M-W

Plenary.

It means unqualified or absolute control.

You can consider the following set of words:

• supremacy

• authoritarian

• totalitarian

supremacy (noun)

supreme authority or power.

authoritarian (adj.)

of or relating to a governmental or political system, principle, or practice in which individual freedom is held as completely subordinate to the power or authority of the state, centered either in one person or a small group that is not constitutionally accountable to the people.

totalitarian (adj.)

of or relating to a centralized government that does not tolerate parties of differing opinion and that exercises dictatorial control over many aspects of life.

[References - Dictionary.com]

Note that authoritarian and totalitarian are synonymous with neutral to negative connotation.

To legislate

to mandate, establish, or regulate by or as if by legislation (Merriam Webster)

Implicit in legislating is the authoritative act of establishing of laws.