The cedar, the strip of crimson, and the hyssop

Why sprinkle the leper using these three? We might say that this is a chok, and we have know way of knowing. Or that it is a chok, and so there is no purpose, other than to fulfill the arbitrary Command of the King. Or we could suggest that it has some magic, or mystical power. I am not sure can really say that this is a cure for the leper, for this happens after the kohen determines he has been cured, but perhaps this is an additional cure, after the disappearance of the physical symptoms, in which case these items have some natural herbal impact on the condition. (Tanchuma does say לפיכך מתרפא על ידי אזוב.) Or else each of these three might symbolize something. If the last is true, then we can derive meaning from their use in this ceremony.

According to Rashi, relying on Arachin and on Tanchuma, they refer to haughtiness and lowliness. Thus,

a cedar stick: Because lesions of tzara’ath come because of haughtiness [symbolized by the tall cedar]. — [Arachin 16a]		ועץ ארז: לפי שהנגעים באין על גסות הרוח:
a strip of crimson [wool], and hyssop: What is the remedy that he may be healed [of his tzara’ath]? He must humble himself from his haughtiness, just as [symbolized by] the תּוֹלַעַת [lit., “a worm,” which infested the berries from which the crimson dye was extracted to color wool], and the [lowly] hyssop. — [Tanchuma 3]		ושני תולעת ואזב: מה תקנתו ויתרפא, ישפיל עצמו מגאותו, כתולעת וכאזוב:

There is a pasuk in Yeshaya (second perek) about how haughty/lofty the ceder is,

יב  כִּי יוֹם לַיהוָה צְבָאוֹת, עַל כָּל-גֵּאֶה--וָרָם; וְעַל, כָּל-נִשָּׂא וְשָׁפֵל.	12 For the LORD of hosts hath a day upon all that is proud and lofty, and upon all that is lifted up, and it shall be brought low;
יג  וְעַל כָּל-אַרְזֵי הַלְּבָנוֹן, הָרָמִים וְהַנִּשָּׂאִים; וְעַל, כָּל-אַלּוֹנֵי הַבָּשָׁן.	13 And upon all the cedars of Lebanon that are high and lifted up, and upon all the oaks of Bashan;

so it makes for good symbolism that the Biblical text itself recognizes. Besides granting significance to these three items, this also helps us recognize the spiritual rather than physical nature of the malady. And also, the spiritual nature of the cure. From Rashi's explanation of the crimson and hyssop, it appears that humbling himself from his haughtiness is what will heal him from the illness. Thus, there is a religiously meaningful message to take away from this otherwise confounding ritual.

The Midrash Tanchuma discusses this symbolism:

ועץ ארזהארז הזה אין גבוה ממנו. ולפי שהגביה עצמו כארז, באה עליו הצרעת.

דבר אחר:
אמר רבי שמעון בן אלעזר:
על גסות הרוח הצרעת באה.
שכן את מוצא בעזיהו כתיב: ובחזקתו גבה לבו עד להשחית (דה"ב כו טז). ש
וכתיב: ובזעפו עם הכהנים, והצרעת זרחה במצחו (שם שם יט).
האזוב הזה אין באילנות שפל ממנו. ולפי שהשפיל עצמו, לפיכך מתרפא על ידי אזוב. 

In terms of medicinal uses, Wikipedia has the following for hyssop, but I cannot figure out or find any medicinal use for cedar of crimson-dyed wool:

Medicinal uses

As a medicinal herb, hyssop has soothing, expectorant, and cough suppressant properties.^[2] The plant also includes the chemicals thujoneand phenol, which give it antiseptic properties.^[3] Its high concentrations of thujone and chemicals that stimulate the central nervous systemcan provoke epileptic reactions when taken in high-enough doses. It has been also used in the formulation of eye drops and mouthwash.

Herb hyssop has also been observe to stimulate the gastrointestinal system ^[4].

Bechor Shor develops the symbolism in much more detail:

ועץ ארז ושנ י תולעת ואזב . - ארז גבה
שבאילנות ואזוב נמוך, סימן שמגביהות בא
לנמיכות,־ ומי גרם לו החטא, שהוא כשני
תולעת, כדכתיבאם יהיו חטאיכם כשנים
ועתה מחל לו הקב״ה וחוזר למקומו ולגבהותו.
ושוחט הצפור ומערב דמה במים חיים, לומר,
שהמת הוא המצורע שהוא חשוב כמת, דכתיב
אל נא תהי כמת, יתערב עתה עם החיים לבא
במחנה ולהיות כשאר בני אדם. ושולח הצפור
האחת על פני השדה׳ לומר המצורע שהוא
יושב בדד כצפור בודד על גג ואסור ונקשר
מלבא עם שאר בני אדם, עתה הותר לבא עם
חבריו, כמו הצפור שיהתה קשורה בידי אדם
ועתה משולחת על פני השדה לילך ולעוף עם
חברותיה.


In terms of these three items, the cedar is the tallest of trees and represents loftiness, גבהות. This is not something bad, in and of itself. (Thus, Bechor Shor differs from Rashi and Tanchuma in this.) The crimson wool represents sin -- and he demonstrates this, using a pasuk. The hyssop represents lowly stature, which here is not a good thing. What brought him to this lowly stature? The sin. And now, Hashem has forgiven him and brought him to his previous lofty stature.

Ibn Ezra also discusses the features of the cedar and the hyssop, in a way that seems like possible speculation of their import:

ועץ ארז ואזוב -הוא הגדול וקטן במיני הצמחים, והעד מדברי חכמת שלמה ואין צורך לחפש על האזוב, כי הוא ידוע בקבלה. והנה המצורע והבית המנוגע וטומאת המת קרובים והנה גם הם כדמות פסח מצרים.

He notes parallels -- the blood on the doorposts in Egypt was placed via a bunch of hyssop. And para aduma also uses ceder, a strip of crimson, and hyssop.

I am not certain, in all these approaches, whether this is derash, derush, or attempt at peshat. If all these items are symbolic, then discussing the symbolism is indeed a peshat concern.

My Own Suggestion:
Alongside any of the above, I would suggest that there is a practical reason for these three items. After all, these items are being used to sprinkle someone with blood. The cedar is something firm, that the kohen can use to grasp, and direct the sprinkling. The hyssop may extend past the cedar handle, and is flexible, and is thus useful for sprinkling. The crimson-dyed wool is wool, and thus would absorb the blood and water as a sort of sponge. If the former leper must be sprinkled seven times, then it would be good to have it on the sponge. It would not necessarily stay on the hyssop for that long. And perhaps it is dyed crimson because if it were white, it would show stains (of blood, or ash) more readily. Here, it is already red (or orange, it would seem), and we can attribute the color to that.

Not to endorse Christian scripture, but in John 19, when Jesus about to die, he is apparently very thirsty:

29: Now there was set a vessel full of vinegar: and they filled a spunge with vinegar, and put it upon hyssop, and put it to his mouth.

Thus, they used the hyssop as a delivery mechanism (to extend the sponge to him), and the liquid material they wished to convey was tied to a sponge. This might reflect how hyssop and sponges were used, or understood to be used, back in the day. And if so, it would promote my practical interpretation.