"almost absolute" is a correct and usable phrase in written English.
You can use it when something is close to being absolute but not quite. For example, "His control over the company was almost absolute."
So almost absolute pitch here.
In the Assembly, the speaker's authority is almost absolute.
Meanwhile, security agents are allowed almost absolute immunity.
Impunity of the perpetrators of violence is almost absolute.
Super cool: When chilled to almost absolute zero, this chip allows for quantum computing.
She resigned as first reader, although she remained in almost absolute power.
Impunity for such crimes was almost absolute according to a 2009 report by Human Rights Watch.
Speed of ballistic missiles gives the aggressor an almost absolute advantage over any enemy.
The action bespeaks an identification with pursuit, collision and explosion that appears almost absolute.
Nkurunziza is not alone in attempting to use almost absolute political power to extend his rule.
What in Knowlton's day was a decidedly imperfect choice is now an almost absolute one.
