[vi]: shinmeikai, oukoku, meikyo

GG5's examples for sense [1] all use kana. All three kanji forms are in daijr/s and meikyo.

Google N-gram Corpus Counts
| 木霊　　　 |  75,287 |  9.5% |
| 木魂　　　 |  12,560 |  1.6% |
| 谺　　　　 |  16,315 |  2.1% |
| こだま　　 | 684,327 | 86.8% |
|-ーーーーー-+---------+-------|
| 木霊し　　 |  11,319 | 15.1% |
| 木魂し　　 |     459 |  0.6% |
| 谺し　　　 |   1,509 |  2.0% |
| こだまし　 |  61,810 | 82.3% |
|-ーーーーー-+---------+-------|
| 木霊する　 |  13,321 | 14.7% |
| 木魂する　 |   1,755 |  1.9% |
| 谺する　　 |   1,710 |  1.9% |
| こだまする |  73,718 | 81.5% |

@@ -8,0 +9 @@
+<ke_inf>&rK;</ke_inf>
@@ -11,0 +13 @@
+<ke_inf>&rK;</ke_inf>
@@ -18,0 +21 @@
+<pos>&vi;</pos>

no

@@ -21,6 +21 @@
-</sense>
-<sense>
-<pos>&vs;</pos>
-<misc>&uk;</misc>
-<gloss>to echo</gloss>
-<gloss>to reverberate</gloss>
+<gloss>reverberation</gloss>
@@ -30 +25 @@
-<gloss>the spirit of a tree</gloss>
+<gloss>spirit of a tree</gloss>

Is the 1&2 split really needed?

It probably is, but hard to verify as it's not the only こだま.