"The teacher who realizes this will not feel that his work is completed when he has finished the daily routine of recitations, and for a time his pupils pass from under his direct care. He will carry these children and youth upon his heart. How to secure for them the noblest standard of attainment will be his constant study and effort. Ed 281.1"
"Beside those things that are without, that which cometh upon me daily, the care of all the churches."
Both passages discuss the burden and care for others, specifically in a leadership or mentorship role. Paul's concern for the churches mirrors the teacher's concern for their pupils.
"He who discerns the opportunities and privileges of his work will allow nothing to stand in the way of earnest endeavor for self-improvement. He will spare no pains to reach the highest standard of excellence. All that he desires his pupils to become, he will himself strive to be. Ed 281.2"
"Take heed unto thyself, and unto the doctrine; continue in them: for in doing this thou shalt both save thyself, and them that hear thee."
Both passages emphasize the importance of self-improvement and personal example for those in leadership or teaching positions. The idea is that one must embody the principles they teach.
"The deeper the sense of responsibility, and the more earnest the effort for self-improvement, the more clearly will the teacher perceive and the more keenly regret the defects that hinder his usefulness. As he beholds the magnitude of his work, its difficulties and possibilities, often will his heart cry out, “Who is sufficient for these things?” Ed 281.3"
"To the one we are the savour of death unto death; and to the other the savour of life unto life. And who is sufficient for these things?"
EGW directly quotes the verse, indicating a clear and intentional connection.