This question will be a bit complicated. Here are two sentences with two very similar constructions (in bold)
1. 地図は普通、北を上にして[描]{か}かれる。 "Concerning maps, usually they are drawn while you put north at the top" (as literal as I could manage, hope its still correct) From Line 7 in this one https://www.docdroid.net/847v2dg/img-20170413-0001-new.pdf.html
2. 地図に経度と緯度が使用されるようになって、北を上にして地図をかくのが普通になった。 Here's my attempt at translation "Because it has come so far, that on maps longitude and latitude are usually used, it has become usual, that you draw a map while putting north at the top." (again as literal as I could manage to set the individual syntactical parts apart as good as possible) From an exercise about the text in 1.
3. So, in 1 things are pretty distinct. The bold part has an adverbial function, right? In 2, things aren't as clear to me because a noun directly succeeds the bold part. I know that this doesn't necessarily mean anything, but it is a position where attributes are very common. An attribute isn't really possible from my perspective because there isn't dictionary form, but て form. Furthermore, at least in a translation which tries to preserve an attributive relation between 北を上にして and 地図, the result feels ungrammatical: "It has become usual that you draw a you-put-north-top/north-put-top map." The part in italics tries to make things sound at least half-grammatical by translating the unspecified subject into a passive construction.
So TL;DR: 北を上にして acts as an adverbial in both 1 and 2, right? And: Is there a case, apart from one in which the conjunctive forms form a chain which leads up to a dictionary form adjective/verb which modifies a noun, where て form can act as a prototypical attribute, like here: よく考える人は効果的な生き方を見つける。