Is “Did Zheng Bo (Duke Wen of Zheng) ever flee from the Shouzhi alliance, later execute Minister Shen Hou and Crown Prince Hua, and feel grateful for Duke Huan of Qi's virtue?” true?

The Records of the Grand Historian, in the Hereditary Houses, records the true historical deeds of Zheng Bo (Duke Wen of Zheng) such as forming an alliance with Duke Wen of Jin and baring his arm to welcome Chu, and records that he died in the same year as Duke Wen of Jin, but it does not detail the episodes of his killing Shen Hou or Crown Prince Hua. The Chronicles of the Eastern Zhou Kingdoms, in Chapter 24, elaborates in detail the plot that Zheng Bo, because he turned against Qi and served Chu, fled from Shouzhi, later regretted and killed Shen Hou due to Qi's punitive expedition, as well as the fictional details that his Crown Prince Hua slandered him to Duke Huan of Qi, intending to use Qi troops to eliminate the three senior officials of Zheng and seize power, but failed and was killed: "At this time, Zheng Bo sent Zi Hua to attend the meeting on his behalf. Zi Hua, fearing that the Marquis of Qi would blame him, was unwilling to go. Shu Zhan urged him to go quickly. Zi Hua became even more resentful and thought of a plan to save himself. When he saw Duke Huan of Qi, he asked to have the attendants withdraw, then said: 'The government of Zheng is all controlled by the three clans: Xie, Kong, and Zi Ren. The escape from the alliance was actually instigated by these three clans. If, through your lordship's might, you could remove these three ministers, I would be willing to submit Zheng to Qi as a vassal.' Duke Huan said: 'Agreed.' Then he told Guan Zhong of Zi Hua's plan. Guan Zhong repeatedly said: 'No, no! The reason the feudal lords submit to Qi is due to propriety and trust. A son who betrays his father's command cannot be called proper. To come with good intentions but plot to throw his own state into chaos cannot be called trustworthy. Moreover, I have heard that these three clans are all worthy officials, and the people of Zheng call them the 'Three Good Men.' What is valued in a hegemon is to follow the hearts of the people. To go against others and act willfully will surely bring disaster. In my view, Zi Hua will not escape calamity. My lord should not agree.' Duke Huan then said to Zi Hua: 'What the Crown Prince has said is indeed a major matter of state. When your lord arrives, we will discuss it.' Zi Hua's face turned red, and sweat poured down his back, so he took his leave and returned to Zheng. Guan Zhong detested Zi Hua's treachery, so he leaked his words to the people of Zheng. Someone first reported to Zheng Bo. When Zi Hua came to report, he lied: 'The Marquis of Qi deeply resents that you did not come in person and refused to agree to an alliance. It is better to submit to Chu.' Zheng Bo shouted: 'You traitor, you almost sold out my state, and still dare to speak nonsense?' He ordered his attendants to imprison Zi Hua in a dark chamber. Zi Hua dug a hole in the wall to escape, but Zheng Bo killed him, exactly as Guan Zhong had predicted. Prince Zang fled to Song, and Zheng Bo sent men to kill him on the way. Zheng Bo, grateful for Qi's virtue in not heeding Zi Hua, sent Kong Shu to Qi to express thanks and request to join the alliance. Hu Zeng's poem on history says:"