As it rarely appears on its own (i.e. outside of 獅子奮迅), I don't think it should be glossed as an adjective.
We don't typically have "usu. as" notes for nouns that appear in compounds. I think an x-ref is sufficient.

@@ -12 +11,0 @@
-<pos>&adj-no;</pos>
@@ -15,3 +14,2 @@
-<s_inf>usu. as 獅子奮迅</s_inf>
-<gloss>fiercely driven</gloss>
-<gloss>intensely fired up</gloss>
+<gloss>rousing oneself fiercely</gloss>
+<gloss>being intensely stirred up</gloss>

daijs:
勢い激しくふるいたつこと

Note on history with Buddhist preaching:
https://news-mynavi-jp.translate.goog/article/20210412-1832502/?_x_tr_sl=ja&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
「獅子奮迅」の由来
獅子奮迅は、仏教の大乗経である「法華経」や「大般若経」にある言葉です。元は「お釈迦様が情熱的に勢いのある説法や行動をしたことによって、聴衆や外道の方を圧倒する様子」を意味していました。
sankoku: [文]ふるいたつこと。たけりはやること。獅子ーの勢い

https://www.reddit.com/r/ffxiv/comments/1nwf89/japanese_skill_names_differ_widely_on_some_classes/
 獅子奮迅 (literally something like "being riled up like a lion")

http://blog.livedoor.jp/gogo_eigo-denihon/archives/19976477.html
獅子奮迅の勢いで   with great force like a vigorous lion
 cf. 獅子奮迅の働き　work with strenuous efforts


獅子奮迅の解説 - 学研 四字熟語辞典
「奮迅」は、奮い立ってすばやく動き回るさま。出典『大般若経だいはんにゃきょう』五二


https://fof48.com/sisifunjin-imi/
「奮迅（ふんじん）」は勇み立つこと
奮迅とは、勇み立つことです。　わかりやすい言葉で表現をするならば、勇気を出して決意すること。
試合前のボクサーの様子は奮迅しており怖くて近づけない迫力がある。
奮迅の活躍をして上司に褒められた。

英語イディオム表現辞典での「奮い立って」の英訳
興奮して；ワクワクして；奮い立って
訳語 fired up

Not actually good gloss, but *not* "impetuous dash". (defn. just steals fury from "lion's fury"). 奮迅 does *not* mean angry or enraged.
https://ejje.weblio.jp/content/奮迅
斎藤和英大辞典での「奮迅」の英訳
奮迅
読み方 ふんじん
名詞Fury; rage
用例
獅子奮迅の勢
the fury of a raging lion

"impetuous dash forward" seems entirely unsupported. 獅子奮迅 is a compliment, so "impetuous" seems odd. "dash" is not supported by any kokugos.

The reason this gloss has survived this long would seem to be that "奮迅" is not generally used outside of  獅子奮迅, which has a better gloss.  Google news search for 奮迅, it's *all* 獅子奮迅. 

There are no good English glosses of this term that I could find.  The best route I found is to read J-J explanations of "獅子奮迅", which sometimes briefly define "奮迅".  Most just give the daijs definition though. (勢い激しくふるいたつこと)

After many hours and a good night's sleep, "fiercely driven" is what I've gotten to. Open to suggestions.

Note：the sense of "irresistible" in 獅子奮迅 (as in "irresistible force") comes from the *lion*, not from this term.  Also note, this is not productive. The only term that seems to precede 奮迅 is 獅子。

I wonder if something like "drive forward" (as in "internal drive", "intensely driven") got changed to "dash".  Because 奮い立つ, which *every* reference uses to define this term, has to do with being motivated/worked up/etc. Nothing to do with physical movement.

According to refs, (google translate): 獅子奮迅 a word in the Mahayana Sutras of Buddhism, the Lotus Sutra and the Daihannya Sutra. Originally, it meant ``the appearance of the Buddha overwhelming the audience and the heretics by preaching and acting passionately.'' 

The force of the preacher is compared to the force of the lion by analogy.

A blog reference described "奮迅" alone as the frightening state of a worked-up boxer just before his match begins.

Regular uses are 獅子奮迅の勢い, which is *complimentary* about a motivated/driven worker/workforce. As in:
奮迅の活躍をして上司に褒められた。

Here's a blog definition that includes the concept of "drive"(突き進む):
https://koinomikata.com/blog/20190613163621.html
「奮迅」には、「激しく奮い立ち、突き進む様子」という意味がある言葉になります。

All definitions seem to end with さま　こと　or 様子 "the state of". Seems like "adj-no". mirroring  獅子奮迅, is the simplest interpretation.

Again, this term barely exists on its own.

What I will caution is that the term does *not* seem to mean "fury" on its own, even if "fury" appears in glosses for "獅子奮迅". Specifically, the nuances of "anger" or "rage" are not in this term.　 "frenzied" might apply, but to the extent it means "uncontrolled" it doesn't actually seem to apply. (I'm not sure I completely agree with "frenzied" on 獅子奮迅 for the same reason).

@@ -12 +12,6 @@
-<gloss>impetuous dash forward</gloss>
+<pos>&adj-no;</pos>
+<xref type="see" seq="1311100">獅子奮迅</xref>
+<misc>&form;</misc>
+<s_inf>usu. as 獅子奮迅</s_inf>
+<gloss>fiercely driven</gloss>
+<gloss>intensely fired up</gloss>