To capture the main thrust, for our purpose, of the Radomsker's approach (Tiferes Shlomo, Mosdim, Rimzei Purim (27): The obvious reference is to Shaul's war against Amalek, concerning which it says: Vayarev BaNachal (Shmuel I 15:5). The Radomsker, al pi remez, provides us with an approach. Much of what he writes is heavily Kabbalistic, but for our purposes, he notes that Nachal is the acrostic of N-otzer C-hesed L-iAlafim. This Chesed is the Chesed that the Tzaddikim need to draw from Hashem's ancient will (“Ratzon Elyon”) – the will to do Chesed, which was the reason for Creation (“Nachal Kedumim”). Hence Notzer has the same letters as Ratzon. Moshe in gematria is Ratzon as well, and Chazal equate Mordechai with Moshe. In this light, “Veratzui lirov echav” may be taken to mean that Mordechai drew out the ancient will from the “Nachal Elyon” (which Shaul should have done, but did not as he failed in his mission), which taps into the special relationship of Am Yisroel and Hashem and guards them from Amalek. Thus, indeed, Nachal is the antidote to Amalek. Another approach may be gleaned from the Yaaros Dvash, Hemshech Derush 8.
But if we may forgiven a Purim gematria, Nachalah in gematria equals Vayehi Beyemei – the first words of the Megillah. That could be enough of a link, but yesh lihosif. Chazal in Meseches Megillah and in Esther Rabba tell us that anytime Vayehi Beyemei appears in Tanach it is a language that connotes tzarah. The term Nachalah teaches us the principle that Hashem creates the cure before the disease, and kol d'avid Rachamana l'tav. (BTW, kol d'avid Rachamana l'tav is the gematria of Revach ViHatzalah Yaamod – that not just will there be a Hatzalah, but a gain – a Revach – from all our travails.) As we have noted in the past, Amalek in gematria is Safek. He casts doubt on our relationship with Hashem. We must be secure in our bitachon that Hashem is doing whatever he does for our ultimate benefit. Then we experience the Simchah of Purim – Ein Simchah K'Hatoras Ha'Sefeikos. And that leads back to the ultimate, alternative meaning of the word under consideration – to our Menuchah and Nachalah.