《韦氏高阶词典》连词as第二义如下：

2 a: : in the way that

• The letter “k” is sometimes silent, as it is in “knee.”

• In the word “macho” the “ch” should be pronounced as (it is) in “China,” not as (it is) in “Chicago.”

• Knowing him as I do [=because I know him well], I'm not surprised by his decision.

标红的这个例句，和网友的句子基本相同。

现在分词短语knowing him作原因状语（其逻辑主语为句子的主语），as I do 为修饰knowing的方式状语从句（比较分句的亚类）（以我对他的了解程度）。虽然词典括号内将分词短语按照原因状语从句解释，但原因的意味来自于分词本身，而不是as从句。即使去掉as I do, 改为副词well, Knowing him very well, 这个分词短语仍然是原因状语，与as无关。

网友的这个句子也可以按照这个词典例句分析。

And, loving the station as they did, it was only natural that they should be there a good hour before there was any chance of Mother's train arriving,...

=  And, loving the station as they did,  they naturally should be there a good hour before there was any chance of Mother's train arriving,...（naturally 为评注性状语）

loving the station as they did 为现在分词短语作原因状语（loving的逻辑主语为句子的主语they。或者是为改动的原句的主语从句的主语。）as they did为方式状语从句修饰loving（带有比较的意味——以它们对车站的喜欢程度）。

首先，这个句子使用loving 而不是 动词原型love，这肯定是没有错误的（词典例句为证），那么用as引导原因状语从句，loving前置就解释不通了。