First I do not see them as contradictory as the verse from the Brahmavaivartha Purana you quote is only addressing what happens to a soul who has not attained Self-Realization - it does not address what happens to a soul who attains Self-Realization. The verse from the Gita, on the other hand, is addressing what happens to a soul who attains Self-Realization. I think a more appropriate verse from the Gita to compare to the Brahmavaivartha Purana verse is Gita verses 2. 42-45.
If you still insist that the Gita and Brahmavaivartha Purana are contradictory, then Sruti supports Krishna's statement in the Gita, which is not surprising as the Gita is the greatest commentary on the Vedas. When there is a conflict between Sruti and Smriti or Purana, Sruti takes precedence (Sankara's commentary on Brahma Sutras verses 1.2.25, 2.1.1, and others).
And Sruti says - The Mundaka Upanishad II. ii. 8 (Swami Nikhilananda translator, both quotes):
The fetters of the heart are broken, all doubts are resolved, and all works cease to bear fruit, when He is beheld who is both high and low.
And Brihadaranyaka Upanishad IV. iv. 23 says:
This is the eternal glory of a knower of Brahman: it never increases or decreases by work. [Therefore] one should know the nature of that alone. Knowing it one is not touched by evil action. Therefore he who knows it as such becomes self-controlled, calm, withdrawn into himself, enduring and concentrated, and sees the Self in his own body; he sees all as the Self. Evil does not overtake him, but he transcends all evil. Evil does not trouble him, [but] he consumes all evil. He becomes sinless, taintless, free from doubts, and a knower of Brahman.
Finally Sankara's commentary of Gita verse 4.37 says that (Swami Gambhirananda translator):
...the fire of Knowledge itself cannot directly burn actions to ashes, like pieces of wood. So, the idea implies is that full enlightenment is the cause of making all actions impotent.
From the force of the context it follows that, since the result of actions owing to which the present body has been born has already become effective, therefore it gets exhausted only through experience it. Hence, Knowledge reduces to ashes only those actions what were done (in this life) prior to the rise of Knowledge and that have not become effective, as also those performed along with (i.e. after the dawn of) Knowledge, and those that were done in the many past lives.
It should be noted that those actions that have "already become effective" are not experienced like others who are not enlightened. Being fully enlightened, the remaining actions referred to appear as real as a mirage in the desert, the Reality to the enlightened soul being Brahman.