Nobody is forcing you to give. You are trying to be Mevatel the Inyan, and addressing that point is no twist.
How often do you actually give your poor neighbor the equivalent amount of money? Do you only use him out for your argument not to give? This year, perhaps you should Taake give your neighbor something — Amiraso Ligevo’a…
Yes, Tzeddaka is Tzeddaka and Teffilin is Teffilin. The point here is not that you gave, it is what you gave it to. Forget about the fact that you gave money. The idea is to be Marbe K’vod Hatana.
If someone donated a Shaar for the Beis Hamikdash, was that Tzeddaka? What if he had a neighbor that could use the money? Tzeddaka means to give to the poor and it is a great Mitzva. It was not meant to supplant all other Mitzvos, though. If you are Osek in Hashovas Aveida you are Pattur from Tzeddaka. Giving to Hekdesh is it’s own Mitzva, albeit not Tzeddaka. Not every Mitzva done with money is Tzeddaka.
When you give for a cause other than Tzeddaka, the merit lies in what you are accomplishing. You are building or supporting Torah, Meor Beis Medrash, Reishis Hagez or Simchas Rashbi. Nno one is forcing you what to choose, but one doesn’t cancel the other.