There’s no reason to believe Admirals > HK Garling, much less Gorosei Garling. Jiaga performed just as bad against Xebec.
Also, no reason to believe HK Garling > HK Shamrock
Also, no reason to believe HK Garling > HK Shamrock
You got it backwards. There is absolutely no reason to think any Gorosei or HK is above an admiral. The Gorosei couldn't do as much as a sandbagging Kizaru.