I feel Warwick's mental state would be pretty important here. If Warwick truly is mentally handicapped, and Lincoln is right there to see it for himself, it seems he would be less likely to declare for him.
Warwick was absolutely not 'mentally handicapped'. His mental age was pretty much stunted by being imprisoned in the Tower by Tudor. He was kept in almost complete solitary confinement with rare visits from loved ones/his sister, he had no education after this. There is zero evidence that Warwick was anything but a bright young boy before that, educated alongside his cousins at court.
Does he even have possession in this scenario? De la Pole should be at Bosworth and is currently scattered to the winds.
I am sure that his uncle, Edward IV granted him some lands when he made him Earl of Lincoln (not a subsidiary title) and he also benefited from the fall of Buckingham etc during the reign of Richard. De la Pole should not have been at Bosworth, he and his cousins were all sent to Sherrif Hutton for their protection in the 'unlikely' case of Tudor winning the battle.