These are some suggestions.
After the accident, he became keener.
(The comparative of KEEN is not used regularly so it sounds awkward.)
After the accident, he became more enthusiastic.
I went to the STORE to BUY a velvety blanket for myself.
When I went to the store, I bought a velvety blanket for myself.
He always CORRECTS his mistake in the NICK OF TIME.
(The correction happens at the end.)
Is he rushing to do his work?
You could also say, "He always makes a mistake when PRESSED FOR TIME".
He URGED me to stay and WATCH TV with him.
You have to be careful doing this project.
(It is a continuous action.)
You have to be careful when working on this project.
This is so important, I should do it modestly.
This is so important. I should work at a modest pace.
She thought your class was boring, so she SNUCK OUT OF the class.