Menachos 62a - Waving and Shaking the Lulav

The gemara says that the waving of שתי הלחם together with the two sheep is done in all 6 directions, to symbolize holding back bad winds and dew. Rabba comments that this is the same method of waving that is used by the lulav. Tosafos suggests that this style of waving only applies to the שתי הלחם and lulav which are in some way connected to agricultural needs, but not to the waving of the other menachos. Tosafos quoting Aruch raises a question whether we requirement of the Yerushalmi to wave 3 times in each direction requires outward and inward three times (totaling 6 movements in each direction) or outward, inward and outward (3 movements total). The Aruch cites other places where the gemara leaves this type of issue as a question and therefore concludes - ולא איפשיט, וכיון דלא איפשיט עבדינן לחומרא שלש פעמים בכל אחד ואחד. The Aruch seems to assume that the safeik would require us to be machmir. It is not clear why this would be the case. Even if we consider the concept of waving to be d'oraysa, the gemara says that it is only שיירי מצוה and not essential to the mitzvah. Generally, the concept of ספק דאורייתא לחומרא applies when there is a chance that one did not do the mitzvah, but not when there is a chance that one didn't do the mitzvah in it's most ideal way. Why would we apply the concept of ספק לחומרא to something which is only שיירי מצוה? Perhaps we can derive from here that the concept of ספק דאורייתא לחומרא is not just to be sure that you fulfilled the mitzvah d'oraysa. Rather, even on a kiyum mitzvah of the Torah we would say that mi'safeik one should be machmir to ensure that the mitzvah is fulfilled.

On another point - our minhag is to wave 3 times in each direction. R. Elazar Moshe Horowitz (pinsk) points out that the bavli which demands waving the lulav in all directions doesn't mention 3 times, and the yerushalmi which mentions 3 times doesn't demand in all directions. Therefore, there is no source for the minhag to wave the lulav 3 times in each direction (as we do). Even if we assume that the Bavli and Yerushalmi are in agreement with each other, it would be sufficient to wave 3 times in one directions and then one waving in each direction.