Here's how Gouketsu scales above Homeless Emperor (I think).
First lets's get one thing straight. Gyoro Gyoro/Psykos has the ability to measure the power levels of monsters. This is an indisputable fact that's not contradicted by anything.
She was able to measure that Rhino Wrestler had gotten stronger and reached Demon level.
She also measured three other monsters as Demon level with one of them confirming that she has the ability to measure power levels.
It's also stated that the Monster Association cares about raw power above all else. This implies that Gyoro Gyoro (who measures how strong the monsters are) bases her statements concerning the monsters mostly on how powerful she knows they are.
Gyoro Gyoro does admit that she can't measure the power of being on the level of Orochi. However, he is 5-C+ so anyone weaker than that (which is everyone) among the cadres can be assumed to be accurately measurable by her.
With that in mind, here is the actual scaling. I'm just gonna get straight to the point - Psykos thought Gouketsu was above everyone in the S-Class back when she
thought Tatsumaki was at the level of Elder Centipede. Here's why:
- She was shocked that someone could defeat Gouketsu and couldn't think of who could have done this despite King being a possible suspect as his whereabouts during the Monster Association's attack on the cities was completely unknown to her at the time. This scales Gouketsu above Psykos' depiction of King's strength at the time which is at least on the level of Pre-Molt Elder Centipede.
- Gouketsu's death lead Psykos to assume the Hero Association had a secret weapon that she claims is above the S-Class. She claimed this after learning of Elder Centipede's death which her and the others from the Monster Association attributed to King, even thinking that he did it with one attack. Yet Psykos still didn't think King could have been responsible for killing Gouketsu even when she didn't know his whereabouts at the time of Gouketsu's death and still attributed it to the "secret weapon above the S-Class" later. This means that to her (who has measured the power levels of Gouketsu and Elder Centipede due to her making statements about who can fight them) someone with the power to one shot Elder Centipede isn't strong enough to defeat Gouketsu. This is key to the next bit of scaling.
- Gyoro Gyoro thought that she could defeat Tatsumaki (who she thought was Elder Centipede level) in her true form. After Tatsumaki defeated the Gyoro Gyoro puppet and made Psykos think she's actually above the Gyoro Gyoro puppet and therefore above EC level, she thought that Homeless Emperor would need help from Black Sperm to defeat her.
Here's thing, however. For reasons already stated, Psykos thought that the power to one shot an Elder Centipede level monster was not enough to beat Gouketsu. Yet here she thinks Homeless Emperor would need help from Black Sperm to defeat someone who can overpower an EC level combatant.
So basically (From the perspective of Psykos, who knows how strong the MA cadres are):
Gouketsu > Someone that can one shot an EC level monster
Tatsumaki (In Psykos' eyes when her Gyoro Gyoro puppet got overpowered) = Someone that can one shot an EC level monster
Homeless Emperor <~ Someone that can one shot an EC level monster (As Psykos thought he would need help against Tatsumaki at that point in time)
Therefore: Gouketsu > Homeless Emperor
I may have missed something like a statement that debunks this whole scaling shtick so if anyone finds such a thing please say so because I don't want to accidentally be spreading misinformation.