A single word meaning “absolute control over something”
Solution 1:
I'd suggest you reconsider stranglehold, which actually is nowhere near as mild as you think.
stranglehold
A grip around the neck of another person that can kill by asphyxiation if held for long enough.
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
Solution 2:
Plenary.
It means unqualified or absolute control.
Solution 3:
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.
Solution 4:
dominion:
Oxford English Dictionaries:
Sovereignty or control.
‘man’s attempt to establish dominion over nature’American Heritage Dictionary:
Control or the exercise of control; sovereignty: “The devil … has their souls in his possession, and under his dominion” (Jonathan Edwards).
Collins English Dictionary:uncountable noun
Dominion is control or authority.
They truly believe they have dominion over us. [+ over]Macmillan Dictionary:
[uncountable] formal control, or the right to rule over something
At that time the island was under foreign dominion.