Without the formation of the FRR and the Ronin War, the Combine is in slightly better shape as long as the War of 3039 ended in much the same way it did in canon.
That said, if you want the paths the Jaguars and Falcons took in canon to be the "most prestigious," you are seriously changing the nature of the Clans. They were expecting little enough fight from the Sphere as it was, and deliberately chosing to hit weaker opponents means sacrificing an opportunity to prove their awesomeness.
For all the flack the Kungsarme cops, they actually were fairly skilled and quite well-equipped, blending thew Combine's lights with the Lyrans' heavies and assaults. Their preferred combat style and guerilla experience made them a tough opponent for the Wolves and Bears, who both had to find their own solutions to the latter problem.
The speed of the Wolf advance through the FRR is entirely down to the prowess of the Wolves, not the weakness of their opponent; in other threads I have compared the force ratios between Luthien and Rasalhague, or Falcon and Wolf engagements against AFFC commands.
I don't know if the Wolves of the proposed AU are a cut above the rest as they were in canon or not, but if they are they will outpace the other Invading Clans no matter what corridor they are striking along.
Without the FRR, the most prestigious corridors will be along each side of the Lyran and Draconis borders. In canon, the more militaristic Combine was believed to present a better foe than the Lyran Commonwealth, hence Leo Showers chosing it for his Clan to attack. I would expct the situation to be similar in an AU setting; from left to right the corridors would be Wolf, Falcon, Jaguar, and Bear rather than the Falcon, Wolf, Bear, Jaguar deployment schema we're familiar with.
I would also note that much of Tukayyid's success stems from Focht having enough time to essentially terraform the whole planet and craft it into a trap for the Clans. Without that opportunity, I would expect the Bears and Falcons to be able to perform much better.The Jaguars could go either way, since their failure was caused by problems endemic to the Clan, but without as much opportunity to prepare the Com Guard may not be able to manage what they did in canon, either.