Shecheyanu On Lulav

 The Yerushalmi in Sukkah (14a) says כשהוא נוטלו מהו אומר ברוך אקב"ו על נטילת לולב. נתפלל בו אומר ברוך שהחיינו וקימנו והגיענו לזמן הזה.  It is clear the Yerushalmi holds that the beracha for taking the lulav is said before taking the lulav but the shecheyanu is said only at the time of the prayer service.  The Tashbatz (volume 2 #204) says the reason is because the נענעום are שיירי mitzvah and hence it is fitting to say the shecheyanu only before the completion of the mitzvah. It should come out from here that those that follow the practice of the אר"י ז"ל to shake the lulav in the sukkah before the hallel, should only recite the shecheyanu beracha at the time of hallel.  However, the Bavli (46a) holds that the shecheyanu blessing should be recited from the time one puts the lulav together before the holiday.  The Bavli clearly holds that one says shecheyanu not at the time of the completion of the mitzvah, but rather once one the object of the mitzvah is prepared (see there in the Mictam a debate if this is by all mitzvot or only by mitzvot one is happy to prepare.)  So presumably according to the Bavli, the earlier one will say the beracha the better, וצ"ע למעשה.  It also sounds from the Yerushalmi that it is normal practice to take the lulav before the hallel, like the אר"י ז"ל.  

It is possible that even if the principle of the Yerushalmi is true that the shecheyanu should be delayed until the נענעונים, it is still possible to say shecheyanu when taking the lulav before hallel.  It would  depend on the machlokes Rishonim if the main נענעונים are at the time of the beracha or at the time of the hallel, (see Tosfos Sukkah 37b, Ran there vs. Rambam Lulav 7:10 and Tosfos Pesachim 7b etc.)