I don't think the example is needed.

@@ -50 +50 @@
-<gloss>to meet fortuitously (e.g. running into an old friend)</gloss>
+<gloss>to meet fortuitously</gloss>

〈めぐり／巡（り）／廻（り）／回（り）〉〈合／会／逢／あ〉う

Google N-gram Corpus Counts
╭─ーーーーー─┬────────┬───────╮
│ めぐり合う │ 61,193 │ 24.5% │
│ 巡り会う　 │ 45,316 │ 18.2% │ - (kokugos)
│ 巡り合う　 │ 31,304 │ 12.5% │ - (kokugos)
│ 巡り逢う　 │  5,593 │  2.2% │ - (not recorded in refs, but "逢" is somewhat common in this word. see "めぐり逢う")
│ 廻り合う　 │    354 │  0.1% │ - (meikyo)
│ 回り合う　 │    139 │  0.1% │ - (daijirin)
│ めぐり逢う │ 23,557 │  9.4% │ - add, sK
│ めぐり会う │ 10,130 │  4.1% │ - sK
│ 巡りあう　 │  9,325 │  3.7% │ - sK
│ 回会う　　 │  9,808 │  3.9% │ - (false positives from e.g. １回会う)
│ 回合う　　 │    862 │  0.3% │
│ 回逢う　　 │    476 │  0.2% │
│ 回あう　　 │    304 │  0.1% │
│ 廻り逢う　 │    242 │  0.1% │
│ 回り逢う　 │    238 │  0.1% │
│ 廻り会う　 │    225 │  0.1% │
│ 廻りあう　 │    181 │  0.1% │
│ 回りあう　 │     64 │  0.0% │
│ めぐりあう │ 50,139 │ 20.1% │
╰─ーーーーー─┴────────┴───────╯

@@ -18,6 +17,0 @@
-<keb>めぐり会う</keb>
-</k_ele>
-<k_ele>
-<keb>巡りあう</keb>
-</k_ele>
-<k_ele>
@@ -32,0 +27,12 @@
+</k_ele>
+<k_ele>
+<keb>めぐり逢う</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>めぐり会う</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>巡りあう</keb>
+<ke_inf>&sK;</ke_inf>

めぐり合う	61193
巡り会う	45316
巡り合う	31304
めぐり会う	10130
巡りあう	9325
巡り逢う	5593
廻り合う	354
回り合う	139

@@ -27,0 +28 @@
+<ke_inf>&rK;</ke_inf>
@@ -30,0 +32 @@
+<ke_inf>&rK;</ke_inf>