I have read or been told that the time to requeen is Autumn, however this strikes me as odd as you must then overwinter a new queen. Why not requeen in March/April and give the new queen the best months to get established.
You have read from wrong place.
Easiest time is requeen in the middle of summer, when you get local mated queens and nectar is flowing.
Of course, if you buy foreign queens in Spring, you give the imported queen as soon as possible.
In Finland the worst time is in August, when flowers are over and bees fight with robbers. Queen introducing losses will be high.
It is better to move queen changing to feeding time. When the colony is full of syrup, It accepts the New queen without problems.
Some hives do not accept the New queen. They want to rear their own queen. They try to Sting the strange queen through the Cage. When their own queen larvae have been capped, they accept the foreign queen easily.
To cap emercengy queen cell It takes 3 days.
It is sometimes difficult to change the queen which has mated soon after It has started to lay. When the mated queen has layed over 2 weeks, the New hive accepts the queen much more easier than just mated . Mistä queen breedes sell their queens ad soon thei have started laying. Which is too soon.