Human evolutionary innovation for rapidly restoring glycogen, and link to cardiovascular disease?
Summary


We (Homo genus) used a lot more glycogen as we sweated while we foraged.
Our efficient metabolism allowed us to replete our glycogen stores with seemingly little trade-off.
Those same metabolic genes are associated with obesity risk
Obesity is a risk factor for heart disease


Sweat uses glycogen

...and lots of sweating was beneficial for our species survival

I think what you are indirectly asking about, as unlikely as it seems, is sweat production. 

It is known that humans have a large number of eccrine sweat glands compared to other animals, for which glycogen is the primary energy substrate. 
The ability to thermally vent via full-body eccrine sweat glands in this way, in conjunction with bipedalism, allowed foraging in the midday heat when predation is low.
This is limited to the genus Homo (Leiberman, 2015), although it is not clear exactly which mutations are responsible as far as I can tell.
Glycogen stores are more supported by their capillaries, and by extension have faster repletion, in primates in hotter drier climates and indeed in humans (Best &amp; Kamilar, 2018).
Now at this point, you are thinking "Aha! More capillaries mean more pressure on the cardiovascular system and more disease". 
I cannot find any evidence directly linking those two.

A note on glycogen production differences in our close relatives

The 1,4-alpha-glucan-branching enzyme indeed seems similar across close species. 
So either we have relatively larger livers to cope with this, or some complex genetic mechanism produces more of the protein. 
A quick BLAST alignment shows the identity of the 1,4-alpha-glucan-branching enzyme of chimpanzee species at >99% and E~0. The top results are shown below:


Entry   Organism    Organism ID Info            Status

Q04446  Homo sapiens (Human)    9606    E-value: 0.0;   Score: 3,814;   Ident.: 100.0%      reviewed
A0A2R9CB94  Pan paniscus (Pygmy chimpanzee) (Bonobo)    9597    E-value: 0.0;   Score: 3,803;   Ident.: 99.6%       unreviewed
H2QMY2  Pan troglodytes (Chimpanzee)    9598    E-value: 0.0;   Score: 3,803;   Ident.: 99.6%       unreviewed
G3SDH8  Gorilla gorilla gorilla (Western lowland gorilla)   9595    E-value: 0.0;   Score: 3,798;   Ident.: 99.4%       unreviewed
A0A096NQ25  Papio anubis (Olive baboon) 9555    E-value: 0.0;   Score: 3,729;   Ident.: 97.6%       unreviewed
A0A2K6ANP2  Macaca nemestrina (Pig-tailed macaque)  9545    E-value: 0.0;   Score: 3,723;   Ident.: 97.3%       unreviewed
A0A0D9R0S5  Chlorocebus sabaeus (Green monkey) (Cercopithecus sabaeus)  60711   E-value: 0.0;   Score: 3,718;   Ident.: 97.4%       unreviewed
A0A2K5W1V0  Macaca fascicularis (Crab-eating macaque) (Cynomolgus monkey)   9541    E-value: 0.0;   Score: 3,716;   Ident.: 97.2%       unreviewed
A0A2I3GDY3  Nomascus leucogenys (Northern white-cheeked gibbon) (Hylobates leucogenys)  61853   E-value: 0.0;   Score: 3,714;   Ident.: 97.2%       unreviewed
A0A2K5I4Z7  Colobus angolensis palliatus (Peters' Angolan colobus)  336983  E-value: 0.0;   Score: 3,713;   Ident.: 96.7%       unreviewed
A0A1D5R8L3  Macaca mulatta (Rhesus macaque) 9544    E-value: 0.0;   Score: 3,712;   Ident.: 97.2%       unreviewed
A0A2K6KT87  Rhinopithecus bieti (Black snub-nosed monkey) (Pygathrix bieti) 61621   E-value: 0.0;   Score: 3,705;   Ident.: 96.9%       unreviewed
A0A2K6PB45  Rhinopithecus roxellana (Golden snub-nosed monkey) (Pygathrix roxellana)    61622   E-value: 0.0;   Score: 3,699;   Ident.: 96.7%       unreviewed
A0A2R9CB98  Pan paniscus (Pygmy chimpanzee) (Bonobo)    9597    E-value: 0.0;   Score: 3,680;   Ident.: 99.0%       unreviewed
A0A2I3T5K0  Pan troglodytes (Chimpanzee)    9598    E-value: 0.0;   Score: 3,680;   Ident.: 99.0%       unreviewed
A0A2I2ZFX5  Gorilla gorilla gorilla (Western lowland gorilla)   9595    E-value: 0.0;   Score: 3,675;   Ident.: 98.8%       unreviewed
A0A2K5QWD9  Cebus capucinus imitator    1737458 E-value: 0.0;   Score: 3,665;   Ident.: 96.0%       unreviewed
A0A2K6SM68  Saimiri boliviensis boliviensis (Bolivian squirrel monkey)  39432   E-value: 0.0;   Score: 3,661;   Ident.: 95.9%       unreviewed
F7FDF1  Callithrix jacchus (White-tufted-ear marmoset)  9483    E-value: 0.0;   Score: 3,627;   Ident.: 96.0%       unreviewed
A0A2K6ANP4  Macaca nemestrina (Pig-tailed macaque)  9545    E-value: 0.0;   Score: 3,610;   Ident.: 95.3%       unreviewed
A0A2I3MXY4  Papio anubis (Olive baboon) 9555    E-value: 0.0;   Score: 3,607;   Ident.: 96.9%       unreviewed



Although this is only one protein of a multi-protein metabolic pathway, I think there must be something much more complex about how our glycogen is repleted to deal with the higher demand than simple differences in proteins.

Increase metabolism and disease

Humans have benefitted from a "thrifty genotype" when it comes to metabolism (Neel, 1999). 
This, and the well-cited 1962 paper it is based on linking our faster metabolism to diabetes (Neel, 1962), may indeed be the paper you are looking for, but in my personal opinion, it is not very quantitative by today's standards and comes from the days before we had access to genomic data.

Although glycogen is only part of the story, it is generally accepted in the community that humans have an optimised metabolism. In terms of disease related to our metabolic evolution, GWAS showed that the genes that allow our increased metabolic activity is linked with obesity risk factors (Castillo et al., 2017).

To link that to your original question, obesity is linked with heart disease according to, well, everyone that has ever looked at it. Here is an NHS link to show it is a principal part of modern healthcare.

It may not be the exact answer you were expecting, so it will be fascinating if other papers corroborate this more directly.

Big brains need a faster metabolism

The scipop article you may have read could be from Science Daily, however this does not mention glycogen. This covers the Pontzer et al., 2016 paper which shows that we have a faster metabolism and this is linked with our brain size compared to our close primate relatives (another angle to the Leiberman 2015 paper discussed below).
The scipop article goes on to talk about research linking this to an increased risk of heart disease, not mentioned in the original Nature article.