daijs:（１）曲がって入り込んだ所。また、奥まった所。もののすみ。片隅。「川の―」
meikyo:（１）曲がって入り込んだ所。また、奥まって隠れた所。物陰。片隅かたすみ。「川の━に船を着ける」「残る━なく探す」
川のくま	0		
川の隈	0		
道のくま	74		
道の隈	179

It's a Chinese to Japanese dictionary, i.e. those 曲 and 阿 entries are Chinese words, not Japanese. It's not suitable as a reference.
暈 is still visible but in a note instead of the kanji field. This is our usual practice for forms that only apply to one or two senses. Daijs/meikyo/smk do it the same way.
目の下に暈 gets zero Google hits.
"bend" is not a separate sense in daijs and meikyo. But this usage appears to be quite rare. It should probably be lower down. Smk describes it as "雅語".

@@ -32 +31,0 @@
-<gloss>bend (in a road, river, etc.)</gloss>
@@ -47,0 +47,5 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<misc>&poet;</misc>
+<gloss>bend (in a road, river, etc.)</gloss>

smk:
㊁濃い色と薄い色とが接する所。〔狭義では、「隈取㊁」の略。例、「━をとる」〕
㊂過労などのために目のまわりに出来る黒いあざのようなもの。
㊁㊂は、「暈」とも書く。
daijs:
③ （「暈」とも書く）色の濃い部分と淡い部分、あるいは、光と陰とが接する部分。また、色の濃い部分。「目の下に―ができる」

1. it's not a chinese dictionary, it's a japanese 中日辞典 made by 三省堂, i think it does have at least some legitimacy to kanji usage
plus, all the dictionaries that have "曲" (which seem to be the minority as most have only 隈 and 暈) also have the "へんぴな所" definition
2. 暈 does seem to be used for dark circles under the eye
3. isn't the policy to keep forms in multiple kokugos visible?
4. i don't think the "bend" can be added to sense 1 as daijr, smk, shinkoku and koj all have it as a separate sense

also this is just my opinion but i don't think restr tags clutter the entry, but i understand the reluctance to use them here as there's no kokugo to follow from

目の下に暈	0

The kokugos have no restrictions for 曲 or 阿. I don't think we can use Chinese dictionaries as a guide to Japanese kanji usage. Also, it's not worth cluttering the entry with restr tags for such rare forms.
I think "bend" can be added to sense 1.
smk has "〈暈〉とも書く" for its "濃い色と薄い色とが接する所" sense but our glosses are more specific. 暈 isn't used for dark circles under the eyes.
The "remote place" sense is archaic. I don't think it's needed.

@@ -6,4 +5,0 @@
-</k_ele>
-<k_ele>
-<keb>暈</keb>
-<ke_inf>&rK;</ke_inf>
@@ -18,0 +15,4 @@
+<k_ele>
+<keb>暈</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
@@ -27 +26,0 @@
-<stagk>隈</stagk>
@@ -32,0 +32 @@
+<gloss>bend (in a road, river, etc.)</gloss>
@@ -35,2 +34,0 @@
-<stagk>隈</stagk>
-<stagk>暈</stagk>
@@ -38,0 +37 @@
+<s_inf>also written as 暈</s_inf>
@@ -44,2 +42,0 @@
-<stagk>隈</stagk>
-<stagk>暈</stagk>
@@ -48 +45 @@
-<s_inf>usu. as クマ</s_inf>
+<s_inf>oft. written as クマ</s_inf>
@@ -53 +49,0 @@
-<stagk>隈</stagk>
@@ -61 +56,0 @@
-<stagk>隈</stagk>
@@ -67,14 +61,0 @@
-</sense>
-<sense>
-<stagk>隈</stagk>
-<stagk>曲</stagk>
-<pos>&n;</pos>
-<gloss>remote place</gloss>
-</sense>
-<sense>
-<stagk>隈</stagk>
-<stagk>阿</stagk>
-<pos>&n;</pos>
-<s_inf>orig. meaning</s_inf>
-<gloss>bend (in a road, river, etc)</gloss>
-<gloss>curved location</gloss>

dicts that only have "隈": sankoku, smk (also 暈), meikyo (also 暈), shinkoku, obunsha, saito, iwakoku
dicts that have "曲" and "阿": daijr/s, koj, nikk

1. (三省堂)超級クラウン中日辞典 for 曲
4th def:
語素（形態素）へんぴな所.
乡曲片田舎.

2. (三省堂)超級クラウン中日辞典 for 阿 ē
2nd def:
名詞文語・書面語くぼみや曲がった場所.
山阿山の奥.

Google N-gram Corpus Counts
╭─ーーーーーー─┬────────┬───────╮
│ 目の下にクマ │ 15,919 │ 68.0% │
│ 目の下に隈　 │  4,327 │ 18.5% │
│ 目の下にくま │  3,165 │ 13.5% │
╰─ーーーーーー─┴────────┴───────╯

from my analysis:
- "曲" refers to remote places (point 1 + all the dicts that have it also have a definition for "へんぴな所"), added new sense (which is present as 古語 in shinkoku as well)
- "阿" refers to bent/curved places (point 2, similar defs in multiple dict), added new sense (should be original meaning according to smk)

@@ -7,0 +8,4 @@
+<keb>暈</keb>
+<ke_inf>&rK;</ke_inf>
+</k_ele>
+<k_ele>
@@ -8,0 +13 @@
+<ke_inf>&rK;</ke_inf>
@@ -11,0 +17 @@
+<ke_inf>&rK;</ke_inf>
@@ -15,0 +22,4 @@
+<r_ele>
+<reb>クマ</reb>
+<re_inf>&sk;</re_inf>
+</r_ele>
@@ -16,0 +27 @@
+<stagk>隈</stagk>
@@ -23,0 +35,2 @@
+<stagk>隈</stagk>
+<stagk>暈</stagk>
@@ -30,0 +44,2 @@
+<stagk>隈</stagk>
+<stagk>暈</stagk>
@@ -32,0 +48 @@
+<s_inf>usu. as クマ</s_inf>
@@ -36,0 +53 @@
+<stagk>隈</stagk>
@@ -43,0 +61 @@
+<stagk>隈</stagk>
@@ -48,0 +67,14 @@
+</sense>
+<sense>
+<stagk>隈</stagk>
+<stagk>曲</stagk>
+<pos>&n;</pos>
+<gloss>remote place</gloss>
+</sense>
+<sense>
+<stagk>隈</stagk>
+<stagk>阿</stagk>
+<pos>&n;</pos>
+<s_inf>orig. meaning</s_inf>
+<gloss>bend (in a road, river, etc)</gloss>
+<gloss>curved location</gloss>