There are very few people who speak like - what many people think the queen speaks like. The queens speech has changed from the days when the pathe films were made. and there are not many speakers who speak like that now but you are right there are some.
Your English writing is excellent and very natural.
1. I was just going to have some fun by/with creating parodies with their "dialect".
2.I was just going to make fun of their "dialects"
it is a very common error that learners make.
1= you are going to have fun for your own amusement.
2 = you are going to make fun at their expenses to belittle them to be cruel, or also to have fun and amusement, for your own pleasure as well.