First, the three month campaign is NOT impossible, it's doable even though the beiyang government got a buff against japan to make it even harder to win.

So basically, to win, dedicate the entire japanese army to qingdao while utilizing the combined army of all your puppets and send them over to the manchurian front. The air has to be focused mostly on the south, with the rest going to the north so you can distract their units there. The initial shangdong offensive is a little harder due to beiyang getting buffed, but you can still win it.

The strategy is to capitulate them, and not take the cities required to win. Most of their cities that have high victory points are located in the easily accessible east of the country where you can take them.

Beiyang will focus mostly on the shangdong front, which has actual supply for you unlike manchuria and due to their poor army quality, you can shred them easily while encircling some of their units.

Once the beiyang government capitulates, annex all their cities and release them as a puppet from your decision and bam, you won.

Though, keep in mind japan is not intended to win, at all. As such, winning means you broke the game (zheltorossiya's focus starting relies on japan losing, but since you won they experience a soft-lock, along with the fact china now no longer works as intended.)

But hey, you can go conquer asia to your hearts content as you skipped the civil war.