This problem is not new and is a relatively minor exposure to the sort of issues that TZ conversion constantly needs to deal with. Different parts of the world have different dates that they adopt (or don't adopt) DST and some nations have changed this date in the past.

Use a library, do not roll it yourself, do not try to outsmart tzdata... if you think you could then please volunteer for this project and either become a new Chronomancer[1] or get disabused of that misconception.

1. It's a legal title, people actually have to call you a Chronomancer if you've contributed to tzdata, it's the law.