I don't think the x-ref is needed.

@@ -13 +12,0 @@
-<xref type="see" seq="1376200">整然</xref>

GG5; 秩序整然としている be in 「good [perfect] order

We don't usually split "adj-t,adv-to" terms into separate senses. I think a simpler single sense is best.

@@ -11,0 +12 @@
+<pos>&adv-to;</pos>
@@ -12,0 +14,2 @@
+<gloss>in good order</gloss>
+<gloss>in perfect order</gloss>
@@ -15,7 +17,0 @@
-</sense>
-<sense>
-<pos>&adv-to;</pos>
-<gloss>neatly</gloss>
-<gloss>systematically</gloss>
-<gloss>methodically</gloss>
-<gloss>in an orderly manner</gloss>

https://dictionary.cambridge.org/dictionary/english/be-in-apple-pie-order

be in apple-pie order
idiom UK old-fashioned

http://yojijukugo.blog.jp/archives/15335989.html

https://eow.alc.co.jp/search?q=整然と並べられている
整然と並べられている
lie in neat lines（複数の物が）

https://eow.alc.co.jp/search?q=整然と
methodically
methodologically
orderly
shipshape
systematically（計画・分布などが）
tidily


=================
Just a few (of many) google book examples, with google translate:

秩序整然と祝おうとしているのである。 google trans: "celebrate in an orderly manner"

地球と太陽は、秩序整然と運行していて "The earth and the sun operate in an orderly manner."

監査の結論に至った過程がわかるように秩序整然と記録し  "Record the process that led to the audit conclusion in an orderly manner."

艦付のボートは塩頭の両側に同様に二手に分れ、ヘさきを海にむけて秩序整然と列べられている。
The boats attached to the ship were divided into two groups on both sides of Shiokami, and lined up in an orderly manner with their ends facing the sea.

勤勉に秩序整然と行うことで、By doing things diligently and in an orderly manner,

With more context:
勤勉に秩序整然と行うことで、創造性を育み業務の限界を超える環境を作ることができます。By being diligent and methodical...

監査計画については後述するが、要するに監査という仕事は、いきあたりばったりに、その場限りで勝手に実施すればよいというようなものではなく、あらかじめ綿密な計画を立てて、これにしたがって秩序整然と実施しなければならないものである。
I will discuss the audit plan later, but in short, auditing is not something that can be carried out haphazardly and on an ad hoc basis; rather, it should be done in an orderly manner based on a detailed plan.

Removing "apple-pie order" as British *and* old-fashioned.

This is grammatically the same as 整然, and appears to have basically all the same potential glosses. Just mildly reinforced, a bit like "neat & tidy" in English I think.

I don't feel that it is readily apparent how to get from the [adj-t] glosses to the adverbial glosses.  At least, I couldn't do it without research. This applies to the main entry 整然 as well, which I have not edited... But here are some google book examples (more context in refs):
秩序整然と列べられている lined up neatly (ships)
秩序整然と運行していて  moving (together) systematically? (the sun and the earth)
勤勉に秩序整然と行う  conducting diligently and (systematically/methodically)  (an audit)
これにしたがって秩序整然と実施しなければならない  (as above)

eijiro provides adverbial glosses for 整然 under a separate entry 整然と (refs).

@@ -11,0 +12,5 @@
+<xref type="see" seq="1376200">整然</xref>
+<gloss>orderly</gloss>
+<gloss>well-organized</gloss>
+</sense>
+<sense>
@@ -13,2 +18,4 @@
-<gloss>in good (perfect) order</gloss>
-<gloss>in apple-pie order</gloss>
+<gloss>neatly</gloss>
+<gloss>systematically</gloss>
+<gloss>methodically</gloss>
+<gloss>in an orderly manner</gloss>

Remove unsupported yoji tag
-*- via bulkupd.py -*-

@@ -13 +12,0 @@
-<misc>&yoji;</misc>

Kanji Haitani list

Adding yoji tagAdding yoji tag
-*- via bulkupd.py -*-

@@ -12,0 +13 @@
+<misc>&yoji;</misc>