For something that's a short verbal phrase, and almost in line with the single-word request of the question, try make hay.
From Merriam-Webster's definition of make:
: to make use of a situation or circumstance especially in order to gain an advantage
// The candidate made hay of his opponent's scandalous behavior.
As a regular verbal phrase, it has the advantage of being more versatile than the other x of y or to x the y forms of similar sayings.
The example sentence in the question could be shortened considerably with this:
Jane's job was absurdly repetitive and oppressive, but for her family, she tried to make hay.
An additional reference for this is from The Free Dictionary:
To take advantage; to make the most of an opportunity.
Chicago better be careful about turnovers, or you can be sure the defending champs will make hay in those situations.
We'll be able to make hay with so little traffic on the road.
… This is a shortened version of the proverb make hay while the sun shines, which dates from the mid 16th century.