Would you check my sentences and correct them? Does 'note' fix the context?
The searching for the missing child ended on a positive/high note.
Charlton had gone 6 matches without a win and dropped into the relegation zone. Pitt, the coach was sacked then Barton was appointed as his successor. The team got back on track under him, winning the final 3 games that pulled it out of the drop zone. With the victories, it managed to avoid relegation. Charlton seemed to start the next season in the second division but it finished on a positive/high note.
1 I'd use 'ended successfully' or something like that
2 I'd use 'high' there.
I'd use 'high' for a real improvement and 'positive' for finishing something better than expected. For instance, the recent Middle East talks ended with an agreement to meet again- that's not much, but it is a bit positive, so you could say they ended on a positive note, but high note would be too much.