Can We Work Out Astral and Causal Karma Even While on Earth?

I don’t know that our line of Kriya Gurus answered this question directly, but it seems from their teachings that it is most typical for souls to have to complete their astral and causal karma on those higher planes, rather than here on earth.

In Autobiography of a Yogi, there is an extraordinary chapter in which a resurrected Sri Yukteswar explains the workings of the astral and causal worlds to Paramhansa Yogananda:
Chapter 43: The Resurrection of Sri Yukteswar

Sri Yukteswar explains that his spiritual work as a teacher has continued on an astral plane called Hiranyaloka, where he is serving:

… as a savior of astrally reincarnating souls coming back from the causal sphere, in particular, rather than of those astral beings who are coming up from the earth. Those from the earth, if they still retain vestiges of material karma, do not rise to the very high astral planets like Hiranyaloka.

Much like the physical plane, the astral worlds have their own allure, though much more beautiful and subtle than the attachments of the physical plane. Sri Yukteswar explains that:

Just as most people on earth have not learned through meditation-acquired vision to appreciate the superior joys and advantages of astral life and thus, after death, desire to return to the limited, imperfect pleasures of earth, so many astral beings, during the normal disintegration of their astral bodies, fail to picture the advanced state of spiritual joy in the causal world and, dwelling on thoughts of the more gross and gaudy astral happiness, yearn to revisit the astral paradise. Heavy astral karma must be redeemed by such beings before they can achieve after astral death a permanent stay in the causal thought-world, so thinly partitioned from the Creator.

Sri Yukteswar adds:

Only when a being has no further desires for experiences in the pleasing-to-the-eye astral cosmos, and cannot be tempted to go back there, does he remain in the causal world. Completing there the work of redeeming all causal karma or seeds of past desires, the confined soul thrusts out the last of the three corks of ignorance and, emerging from the final jar of the causal body, commingles with the Eternal.

Remember that techniques alone aren’t enough to fully free one from all past karma. Kriya must be combined with deep devotion to God and with the guidance and blessings of a true Guru. Meditation by itself isn’t enough.

There are other ways that we can hasten our freedom from past karma, including prayer and forgiveness, for example.

Yogananda, writing about the teachings of Christ, states that the power of prayer can release us from past karma:

Jesus clearly points out that even thought he law of karma which governs human lives is almost unchangeable, still it can be modified by divine prayer. Human beings, according to earthly law, must necessarily suffer for all their evil actions, but when they tune themselves to God by deep prayer and remember the perfect image within them, then, realizing their divinity, they need not suffer for their past human errors.

And also forgiveness:

Jesus says that one can escape the law of karma by identifying himself with God. Once he is able to do that, he should get divine forgiveness by forgiving his brothers who sin against him. But if that soul, finding divine forgiveness from his own karma by meditation, again becomes human by practicing unforgiveness against his sinning brothers, then he again identifies himself with human life and becomes governed by the inscrutable laws of limiting karma. Therefore Jesus says to every soul to remain divine by being continuously forgiving and loving like God.

So you can see that techniques like Kriya are only one of the tools that are necessary for hastening our freedom from past karma on all levels, physical, causal, and astral.