I agree.

Google N-gram Corpus Counts
╭─ーー─┬─────────┬───────╮
│ 経る │ 163,831 │ 99.9% │
│ 歴る │     197 │  0.1% │Meikyo, Iwakoku, etc. ; [rK]
╰─ーー─┴─────────┴───────╯
Sankoku for を sense 4: 経由する場所をあらわす。
Relevant DOJG entry: https://core6000.neocities.org/dojg/entries/120


E.g. oukoku:
（自下一）
[...]
３：過程をたどる。「手続きを経る」「いくつもの職をへて教師になる」

References are unanimous on 自動詞 for all senses, whether the english translation of 手続きを経る is transitive or not is not a criterion.
I would understand it as an extension of the second sense into the abstract

@@ -11,0 +12 @@
+<ke_inf>&rK;</ke_inf>
@@ -34 +35 @@
-<pos>&vt;</pos>
+<pos>&vi;</pos>

This change marks meaning [3] as vt.

The history for this entry suggests that all of them are intentionally marked intransitive. Reading https://jisho.org/forum/633c8ccb12a5375f9e000000-transitive-slash-intransitive, I'm gleaning that this is because "を can mark an indirect object that the movement occurs through". I'm not a linguist, but I wonder if this reasoning should only apply to [2] (as in 東京を経て) but not [3] (as in 手続きを経る). The English translations do suggest transitivity to me -- though on the other hand, Kotobank marks it as intransitive: https://kotobank.jp/word/経る-625737

@@ -34 +34 @@
-<pos>&vi;</pos>
+<pos>&vt;</pos>

@@ -37,0 +37,1 @@
+<gloss>to undergo</gloss>