Since his Refusal had been defeated, Ulric went the path of out-'Crusading' the Crusaders while he was Khan. Its why he as part of Revival he kept his operational pace high as well as hitting a lot of worlds unlike the actual Crusader Clans. To hit that operational tempo he, or someone in his keshik who was involved in the planning, staged supplies forward with those supply caches in frontline systems- not sure if we were ever told if they were un-inhabited or just occupied systems- while his Clusters that had been involved in the fighting consolidated their hold. He also sourced as much stuff locally so the shipments from Clan space was for the vital stuff that could not be found locally. Food, water, uniforms, medical supplies, standard armor, maybe ammo depending on your BTU interpretation, building supplies, tools, ICE fuel, POL, support vehicles (VTOLs, trucks, jeep analogues), and anything else that a army might need on the march- a sort of BTU Sherman's March to the Sea, full scale foraging. Which, since Ulric was waging a logistics war against the Crusaders a handful of Potemkins being added to his logistics planning would have been huge- see
https://bg.battletech.com/forums/index.php?topic=63210.msg1453823#msg1453823.
While not explicitly said, the indication is this is different from the other three Crusader Clans. AFAIK Aiden's story did not cover the Falcons seizing property and looting storehouses for what they needed. We get indications the three Crusader Clans did not care about their logistics and told their tech/merchants to just get everything from the Home Worlds to the IS. The benefit of Ulric's approach is multitude- first since the Clans only care about success, its what he has and means the non-Invaders will listen more in Council than to the Crusader Invaders. Second it puts a LOT of pressure on the invading Crusader leadership, those without bloodnames need combat to get Bloodnamed killed and to prove themselves for advancement. Those with Bloodnames want higher ranked individuals to fall, either through failure or in combat, so they can advance either in Bloodhouse politics or in Clan rank. This is why Aletha was able to replace the Khan after she was elected, the core of the Ghost Bear touman was disappointed in their showing in the Invasion and wanted new leadership to get the Clan on track. The final advantage is the one most people acknowledge, it forced the Crusaders to hurry up their assaults which resulted in more casualties and equipment damage- along with damage to the Crusader's reputation.
When Ulric became ilKhan . . . well, then the plan was cranked up to 11. Natasha and Garth Radick kept up the pace of the Wolf assaults to keep the pressure up. ilKhan Ulric increased the pressure on the Crusaders using his new powers. He added to the invading Clans by pairing enemies with the two strongest Crusader Clans which increased the competition for invasion targets and would add to the dissension in the Falcon & Jaguar ranks- not sure it really had a affect on the Falcons since Crichell was such a operator but the Jaguar's constant change of Khans and the election after Tukayyid would indicate it did work in that Clan. Ulric also negotiated the proxy fight that we know offered such enticing rewards but exploited the other Clans' weakness, and even with Ulric's logistics work the Wolves were not sitting too much better in the supply department.
Orwell, Ulric won since until Seth War followed Alaric's plan (another March to the Sea!) the Clans as a whole had not managed to break past the Truce line for the most part. A third of the Clans he knew were destroyed (Burrocks, Spirits, Mandrills, Hellions, Vipers, Jaguars), more were subsumed by the IS/Peri pops aka capturing the fly paper (Bears, Ravens, Scorpions, Cats, Warden Wolves), or abandoned any present moves against the IS (Adders, Coyotes, Cobras, Lions) This left the Crusader Wolves, Falcons and Horses . . . and Malvina's Falcons is what Ulric most feared for the future.