True. However, I'm thinking that if the Sui didn't fall, the Turks wouldn't be as effective. I can't imagine them approaching Luoyang under the Sui the way they nearly attacked Chang'an during the early Tang. On the other hand, the Eastern Turks collapsed by around 630. I'm thinking that this alt-historical Sui Dynasty, if it outlives the Eastern Turks, could be strong enough for the task of conquering Koguryo, though of course I can't say for certain.
Well, I'm not really sure about the conflicts between the Turks and China, but I think that Chang'an was attacked around 600, and although there was a civil war between the Western and Eastern Turkic factions, they might have been more united if the Sui had thought about launching a campaign against them first.
While it's not impossible, though maybe not likely, for this *Sui Dynasty to send out diplomats to Paekche or Silla, I assume that if these countries are interested in winning, they might take the initiative instead. I'm not sure if it's likely, since it depends on differing relations between the three kingdoms, but what if during this time Koguryo and Silla attack Paekche, prompting Paekche to ask for assistance from Yamato and China? Instead of the historical battle of Baekgang with China and Silla versus Yamato and Paekche, we have China, Paekche, and Yamato versus Koguryo and Silla.
It would have been extremely unlikely for Goguryeo to ally with Silla. As FDW mentioned, Yamato had close ties with both Baekje and Goguryeo, so it would be hard-pressed to choose a side, while if Baekje did manage to retake the Han River Valley, which would probably be unlikely, then it might have been somewhat possible for a Goguryeo-Silla alliance. In OTL, however, the biggest issue was a territorial dispute between Goguryeo and Silla. As I stated before, Kim Chunchu, who would later unify the peninsula south of the Daedong River, went to Goguryeo in 642 in order to propose an alliance due to Baekje's string of successes against Silla. However, Yeon Gaesomun made a counter-proposal in which Silla would hand back part of its northwestern territory that Goguryeo had lost during its wars with the Sui, possibly because Goguryeo wanted to attack Baekje directly instead of going through Silla or solely using naval forces. However, if Silla accepted this proposal, this would have potentially meant that the Han River Valley would be in jeopardy after Baekje was conquered, so it was forced to go to the Tang and negotiate.
This source says the 598 affair was a joint operation between Koguryo and the Mohe/Malgal (haven't decided which one I'm going to call it). I haven't read through it enough to know if it's credible though.
Yes, but the Mohe had been culturally influenced by Goguryeo enough to have been considered as something less than a tributary state, so it doesn't really explain Goguryeo's long-term strategy. Goguryeo also had consistently used both Khitan and Mohe allies during previous battles with states in China and the southern Korean Peninsula.
Okay, it's just that you said "then break through two lines of fortresses to successfully invade Pyongyang," while I would technically argue that China could have taken Pyongyang with a naval landing and then a land assault (wasn't it abandoned? Or am I thinking of another city? Or was that during the war with Tang and not Sui?), though I don't think that's a very Chinese-style of warfare, and I don't think it would lead to a lot of success either. On the other hand, I think Koguryo can't just hope that storms in the Yellow Sea are going to scatter the Chinese fleet every time.
I didn't mention it before, but I read somewhere that the storm during the first naval battle was probably fabricated in order to lessen the magnitude of the Sui's defeat. As a comparison, Taizong was also so upset with his defeats against Goguryeo that he requested to look at the records about him, and possibly rewrote some of them. Regardless, Gang Isik managed to defeat the Sui in the first invasion with a navy of about 50,000, and he probably would have repulsed more if the Sui had attempted to do so. Even if the Sui navy had been successful and captured Pyongyang from a naval assault, Goguryeo forces probably would have simply withdrawn and attempt to hold out from its fortresses in the Liaodong Peninsula. After all, the capital in Guknae Fortress had been sacked twice before, yet Goguryeo managed to come back each time, so it really wouldn't have make sense for Goguryeo to sue for peace when they had plenty of other fortresses remaining.
In OTL, Goguryeo fell due to a power struggle between the three sons who succeeded Yeon Gaesomun, which would not have occurred if the monarchy had been retained. The oldest, Yeon Namsaeng, defected to the Tang and aided them in systematically conquering strategic fortresses, which would have been extremely hard for the Tang to carry out alone. Any hopes of holding out were eventually dashed because Silla attacked from the south soon afterward, which caused the state to capitulate after the capital fell.