Why is there volitional form and か in this sentence: 筋肉痛に悩まされつつも一通り終え、そろそろ家に戻ろうかというところにリーゼがやってきた。


Sentence:

> 筋肉痛に悩まされつつも一通り終え、そろそろ家に戻ろうかというところにリーゼがやってきた。

My translation attempt:

> Despite the muscle pain he finished as usual, about the time he intended to
> come back home, Rize turned up.




> (0) そろそろ家に戻ろう **か** というところにリーゼがやってきた。

  * the questioner: ..., about the time he intended to come back home, Rize turned up.
  * kandyman: Just as he was thinking of heading home, Rize came along.

If you interpret the interpretation by the questioner or in the kandyman's
answer, it seems that one of the following (1) to (4) could be applied in
Japanese.  
Of course, I think that both interpretations reflect the meaning of (0) in the
original text, but the problem is that they do not directly explain the
existance of "か" along with a volitional form in (0) posted as a question.

> (1) そろそろ家に戻ろう **とするタイミングの** ところにリーゼがやってきた。  
>  (2) そろそろ家に戻ろう **と考えている** ところにリーゼがやってきた。  
>  (3) そろそろ家に戻ろう **と考えているタイミング** にリーゼがやってきた。  
>  (4) そろそろ家に戻ろう **と考えているちょうどその時** にリーゼがやってきた。

As for the か, I think it is a short form of the following phrases like:

> (5) そろそろ家に戻ろう **かどうか** というところにリーゼがやってきた。  
>  (6) そろそろ家に戻ろう **かどうしようか** というところにリーゼがやってきた。

### EDIT

As I got a comment from personanongrata, I reconsidered my answer.

In the interpretation of "か" in (5) and (6) in my original answer, besides the
option to return home, there is another option not to return home, but from
the context of (0), there is, I think, only an option to return home.
Therefore, I judged the interpretation of (5) and (6) as mistakes, so I would
post (7) or (8) as the interpretation of "か" instead.

> (7) そろそろ家に戻ろう **かなあ** というところにリーゼがやってきた。  
>  (8) そろそろ家に戻ろう **かなあと考えている** ところにリーゼがやってきた。




If it was just 戻るところ it would mean that he was actually in the process of
starting his return. The decision to return has already been made and it is
now about to be carried out.

By using 戻ろうか it indicates that the person was intending to return, or in the
process of considering it, but had not begun the actual movement of returning
since the decision has not been finalized. In addition, the というところ indicates
that it was just at that moment when the person was considering returning that
Rize turned up.

I'd translate it like this:

"Although plagued by muscle pains, he finished up as usual. Just as he was
thinking of heading home, Rize came along."

