How to use に with "masu-stem (連用形 stem) + に + Verb" structure


Could somebody provide a bit more explanation, possibly giving correct and
incorrect examples on how to use に with "masu-stem (連用形 stem) + に + Verb" as
illustrated in the following examples?

Both feel intuitively sound but I cannot find an explanation that allows me to
compose my own sentences.

>   1. なお、本状と行き違いにお支払い済みの場合はお許しください
>
> Please forgive us in the case that payment has been completed "in crossing"
> with this letter(ie while the letter was still on its way)(note1)
>
>   2. そして通りすがりに鐘をならしつつ、かれは隣室へと一同を先導した。
>
> And ringing the bell in passing, he led the way into the adjoining room
>
>

**What are my thoughts?**

  1. に indicates that (と)行き違い describes the manner in which お支払い(済み) was done and seems to be the same as the に below (despite お支払い済み appearing not to be a verb)
  2. It looks similar to Nにして／連用形 stemながらにして which "indicates a time[/point] when a surprising [event] takes place"(note2) but does not fit the pattern.
  3. It seems to be different from the familiar 「を買いにいく」which has a clear purpose and direction ("to go to buy something") or the other use of this pattern covered in another question "How does one use the “[V ます stem] に [Vタ]” pattern (as in 待ちに待った)?".
  4. Its not an "N1にN2 pair"(because I asked in a previous question)

* * *

*Note1: This often appears in payment reminders. The English equivalent is more likely to be "Please ignore this notice if you have already paid (this card and your payment have crossed)" but I think this literal translation is more helpful to solve the question.

Note2: From Dictionary of Advanced Japanese Grammar*




I feel in this specific case, it might be possible to discern a pattern.

> ~に~~する

can be used to say "while doing -, I did --". For example,

> 登校中に便意をもよおした

This translates to "while commuting to school, I felt like going to the rest
room." I think this is almost certainly the case for the second example in the
OP.

It may actually not be fitting to interpret the first example the same way,
since the expression used to mean "in crossing" doesn't really describe what
the person is doing, but more like how s/he does thing in relation to the
other action. So in that case, the usage of に there is describing how the
thing is done. For example,

> 迅速に支払いをした. (He paid promptly.)
>
> 上手に作文を書いた. (He wrote a paper well.)
>
> 虹のように弧を描いた (He drew an arc like a rainbow.)
>
> 行き違いに手紙を送った (Their letters crossed.)

Obviously the last example is very close to the first sentence in the original
post.

I warn you that I have never been trained to teach Japanese to a student. So
take this as some perspective of a native Japanese おっさん. My intention is just
to point out that the way that I suggest at least sounds natural to a native
Japanese speaker. Not meaning to offer any insights from linguistic
foundations (I wish I could!).

