It seems to me like perhaps we should learn the Torah of the karbonot whenever we want to work on Teshuvah. This is especially relevant as we are now in the book of VaYikra which contains the teachings pertaining to the various offerings.
HaShem so much wants our Teshuvah and our well-being that He will accept something that is no more than a written account of what should be done as a full apology. This is interesting in the light of what Shmuel HaNavi says to Shaul HaMelech when he saved the animals of Amalek to offer as sacrifices to HaShem: You think HaShem wants your sacrifices? All He wants is for you to listen to His Word.
So, by learning the Torah of the karbonot (Torah being the Word of God) when we cannot currently actually offer the sacrifices, perhaps we are acknowledging the depth of Shmuel HaNavi's words.
On a semi-related note, the RaShaSh z"l Rav Shalom Sharabi, regarding the Tefillah and the Seder on Pesah, explains that mitzwoth that are performed through speech alone illuminate with the inner aspect of HaShem's light, whereas mitzwoth performed through physical acts illuminate with the outer aspect of HaShem's light. So, perhaps in our case here, even though we cannot bring down the outer light, through actually performing the sacrifice, by reading the Torah regarding the sacrifice aloud, we can still awaken and draw down the inner light.