I can't help you with your question regarding the channel crossing except to say that I think your boyfriend's idea of having someone meet you is a good idea.
It is definitely recommended NOT to sedate your animal for a flight (respiratory depressant, they can die). Please don't do it.
We flew United and they won't accept an animal if they suspect it has been sedated, I expect the other airlines are the same.
There is a lot of debate over the whole, cabin vs hold issue for small pets. (Only relevant when flying into mainland Europe, they have to travel as manifest cargo to the UK)
We flew straight into the UK so our cats were in the hold, but given the choice, I would put them there rather than in the cabin.
In the cabin, your cat will have to be in a small carrier, the lights will be on, there will be a lot of noise, other people and bustle whereas in the hold, they will be in a large carrier, with just the lull of the engine for company. They will be likely just to sleep through the journey. Put an old t-shirt of yours in with kitty for comfort