Sorry to hear that your sites are in a sad state. UTF-8 has been around since 2002 if memory serves me well... It's the most popular character encoding for the web, it supports all possible characters. Maybe we can help you port your sites to this standard.
Anyway, I searched a bit about this issue and found this article that seems to contain helpful info: https://www.saotn.org/php-56-default_charset-change-may-break-html-output/ (some answers on stackoverflow also seem to refer to it). Try that one out and let us know if that fixes the issue.
[I found an interesting chart about UTF-8 popularity on https://en.wikipedia.org/wiki/UTF-8]