You do realize Jiraiya could easily summon Gamabunta to pin the Hachibi down, which would cancel his Bijuu Dama? After that use Dark Swamp to solidify its immovability.
And the Eight Tails Whirlwind is not finishing off Sage-Mode Jiraiya. Even in a field with much trees (Obstacles increasing its destructive capacity) simple Jinchuurikis were not fatally damaged, just brought off balance. Jiraiya in his base-form has already shown superior durability, but in Sage-Mode he would easily tank it.
Not to mention he would not even allow Bee to use that, as soon as Bee transforms, Jiraiya sinks him. If he spins, he is only going to be caught in it quicker.