Well, I kinda inferred which Institutes you were talking about by the conversation alone, but the practice of using code numbers for design institutes is something we aren't used to in the West. The Soviets also used a similar system though e.g. OKB-1 was Korolev's design bureau and OKB-51 was Sukhoi's.
I agree that SAC's proposal has more chances of winning the naval stealth competition. CAC is already busy with the J-10 and J-20 and it's a way to keep SAC viable long term. SAC also has more prior experience with naval aircraft due to the J-15. The Chinese carriers are smaller than US carriers, having smaller aircraft means you can carry more aircraft. Once the carriers become equipped with catapults, and the area of operation goes beyond the 2nd island chain though, I would not dismiss the idea of a navalized J-20. Why? Because of range concerns, to strike at longer distances, or to use as a large fleet defender. The US similarly used to have a hi-lo combo with the F-14 Tomcat and the F/A-18 Hornet which was basically dismissed for cost concerns. The F/A-18E Super Hornet isn't a viable replacement for the Tomcat in terms of range, payload, speed, and other capabilities despite being more powerful than the base Hornet. When China surpasses the US economy in GDP (nominal) they'll be able to outspend them militarily.
I agree that SAC's proposal has more chances of winning the naval stealth competition. CAC is already busy with the J-10 and J-20 and it's a way to keep SAC viable long term. SAC also has more prior experience with naval aircraft due to the J-15. The Chinese carriers are smaller than US carriers, having smaller aircraft means you can carry more aircraft. Once the carriers become equipped with catapults, and the area of operation goes beyond the 2nd island chain though, I would not dismiss the idea of a navalized J-20. Why? Because of range concerns, to strike at longer distances, or to use as a large fleet defender. The US similarly used to have a hi-lo combo with the F-14 Tomcat and the F/A-18 Hornet which was basically dismissed for cost concerns. The F/A-18E Super Hornet isn't a viable replacement for the Tomcat in terms of range, payload, speed, and other capabilities despite being more powerful than the base Hornet. When China surpasses the US economy in GDP (nominal) they'll be able to outspend them militarily.