A good reasoning. I would like to hear more of your thoughts on why Gaozhong was so keen to make peace with Jin that he was willing to kill his best general, in the middle of a campaign, when Song was winning all their battles?
That you have to find answers in GaoZhong's biography
a member of the royal family who had been taught that they were the descendants of heaven and they were the living gods and dragons, it would be pretty difficult for him to think he couldn't beat Jin.
You need to understand chinese system of succession. Not all sons of the Emperor were treated equally. Only the firstborn of the Queen has the right to the throne. All other sons, depending on how their mothers fared, were either made prince consorts or, in the worst cases, seen as potential usurpers and living in house arrest.
GaoZhong's mother was not the Queen, in fact, his mother was much disliked by his father, Emperor HuiZhong. When GaoZhong was growing up, his father rarely visited him and his mother. As a result, Young GaoZhong led a lonely, precarious life, in the shadow of his father and big brother who are destined for the throne. This experiance is very important in shaping his personality and later life even more so than running away from Jin. GaoZhong, or ZhaoGou as his real name, has a very shadowy, pessimistic personality. Added on top of that, he was infertile(speculation points to the trauma of being chased by Jin as the cause). So, he was insecure as well.
All in all, GaoZhong certainly don't believe himself to be a demigod.(none of Chinese emperors actually believe so, that was a russ created to justify there rule to the peasants.) In all probablity, he viewed himself as an unwanted son, who picked up the crown thanks to the chaos created by Jin.
Yet, as evil and as smart as Qin Hui was, he never even attempted to frame Yue.
No, he did frame Yue as a traitor. He gathered three major evidences and got Yue's former lieutanent to testify aginst Yue. He tortured Yue and his son in order to secure their confessions. But I think it was fair to say Qin Hui did not expect Yue's former comrades to buy his story. Yue Fei's moral uprightness was renowned. So the "treason" was used more as an excuse than a illusion. "mo xu you" was not Yue Fei's offcial crime, It was something Qin Hui said when Hanshizhong appealed to him in Yue's defense, check my previous post as to what it means.
The mystery is China was winning and winning big. When Yue was called back, most of what was Song China and was taken over by Jin was already recovered by Yue.
There are a couple points to be made here.
First, in ancient times, information was not as easy to obtain as it is now. GaoZhong did not have satellite photographes of the battlefield or any photographs for that matter. Whatever the victories Song scored, he has to take Yue Fei's word for it. GaoZhong had witnessed firsthand how weak, undisciplained and cowardly the Song's soliders were in the early years of Jin invasion. Now, Yue Fei was writing him claiming these colossal victories after colossal victories and demanding reinforcement when Yue had already consolidated more than half of all Song's force under his command, what kind of Emperor was he not to be suspicious?
Second, taking a strategic view, Song cannot completely eliminate Jin no matter how successful the military operations went. Jin was not an agricultural civilization like Song. The best case scenario for Song was to drive Jin north into Manchuria where they originated and what then? Song would gain a lot of useless land(the economic center of China at that time had already moved south of Yangzi) which she has to guard against Jin. It was very costly(way more for Song than for Jin) to conduct wars and keep a large standing army. In fact, It wouldn't be a bad idea for Song to keep a state to her north that she has working relations with and shield her from all the possible incurssions from nomadic tribes. That state used to be Liao, and Jin could fill that hole, that would, by far, be the most preferable outcome for Song's security and economy. If the ultimate political solution is to co-exist with Jin, what a better time to neogiate peace when you just scored a big victory?
Third, GaoZhong is a very pragmatic ruler. He wasn't the chosen successor of throne so He don't really care to be recognized as the Dragon-born, the Emperor of China or the meant-to-be ruler-of-all that sort of thing. In Song-Jin peace treaty, GaoZhong even agreed to call the King of Jin "Father Emperor"(OMG). In Chinese trandition, a person's father was practically that person's God. So calling someone other than your father "father" is the ultimate humiliation.(GaoZhong went down chinese histroy as the "Son Emperor"). From this, you can just see how much ball this so-called "Emperor" really has.(hint: GaoZhong never sired any offspring).
Finally, GaoZhong's sucking up to Jin worked out at the end. Although there was another war after Yue Fei was killed, both Song and Jin eventually realized that neither of them can truely destroy the other. So, they both settled to have what they could before Mongolia conquered China. It's really hard to say whether GaoZhong's decision was a wise one. That is a question for "If historians". But I think it's safe to conclude Gaozhong has reasons to do what he did. It's not out of pure paranoia like what emperors often have towards powerful generals.
Additionally, emperors were usually extremely protective of traditions. What their ancestors had done MUST be upheld with utmost respect. Yet, Gao Zong's son almost immediately overturned ALL of Yue's supposed "wrongdoing" and gave Yue all kinds of titles that he could possibly give. An 180 deg turn of his father's decision. That was almost unheard of.
Well, Gao Zhong's son Xiao Zhong was pretty ambitous and was pushing for a war with Jin to take back Song's historical capital. So, he, as his father, viewed Yue Fei as a big flag for warmongering. The difference was that He needed to erect the flag that his father had cut down. So, Xiao Zhong sold a story that Yue's death was because of the hoax that Qin Hui had pulled on his father. He made Qin Hui to be the Big Bad while keeping his father's name (almost) intact.