There is previous research for that field of macroevolution.... Horse shoe crabs change slowly and tropical fish change fast.
You are right, it's not just random variation, it's fine tuned by DNA transcription processes which are too developed to be random, so the complexity of the processes leads scientists to think "WTF" regarding epigenetics, transgenerational phenotypic plasticity, paramutation, genetic drift, DNA mutation types, Specifically: "no systematic cross species studies of variation have been conducted (most focus on model organisms)", because the topic is so intense.
You don't have to change the DNA code of alleles to go from a chimpanzee to a human, most of the changes come from pre-existing genes that are varied to produce different results.
The texts for macroevolution fine-tuning of variability talk about: variability, gene flow, constriction, epigenetics, of traits of adaptive significance, of DNA mutations, their mathematical measurement... it can be summarized by this statement:
" variability has been a dilemma of evolutionary biology. Considering the pattern of increased genetic variation associated with environmental clines and heterogeneous environments, selection in heterogeneous environments has been proposed to facilitate the maintenance of genetic variation. No comprehensive models have been developed, likely due to the genetic and environmental complexity of this issue. " ref
Many books are devoted to the subject, so there is lots to read through, and there are mutation-control systems that fine tune variability, so it gets complex:
"... Epigenetic modifications, such as; DNA methylation, together with covalent modification of histones, are thought to alter chromatin density and accessibility of the DNA to cellular machinery, thereby modulating the transcriptional potential of the underlying DNA sequence" ref
There are genetic switches, which vary which DNA sequences are expressed by different species... Humans and chimps are 98% the same, and genetic switches can change the species selectively without having to change the DNA itself... "regulates when and where genes are turned on and off and how much protein they produce. The regulatory machinery works when proteins called transcription factors bind to specific short sequences of DNA that flank the gene, called transcription factor binding sites, and by doing so, switch genes on and off." ref
sharks ahve less less variability than humans and 1.5 times bigger genome...
"The researchers found that the white shark genome contained a lot of genes responsible for maintaining genetic stability — things like DNA-repair genes and tumor-suppressing genes. And when the researchers compared the white shark's stability genes with analogous genes in other vertebrates, they found small changes in the gene sequence that suggest a specific pattern of evolutionary adaptation for these genes in white sharks."
Only a few epigenetic processes for transgenerational epigenetic inheritance have been discovered, which vary species traits independently of the DNA sequence, so we don't even know how they compare between animal families.