I haven't mailed to PCGS or PMG.
But I have mailed several batches to BCS. I used Canadapost "Priority" express service.
Its more expensive than Xpresspost but usually 1 day turn around.
I usually would mail it on Wednesday before they pickup and BCS would have it the next morning.
For insurance purposes I would usually put the notes in a Small box inside a bigger box with padding around it.
Then you can mark insurance up a high as you need. If they ask whats inside.. be creative.
I don't think they will insure "Banknotes"
If mailing to the USA I would probably go with FED-EX. BCS uses Fed-Ex to return the notes to me and they offer insurance even for banknotes.
But I guess it all depends on the value of the notes you are sending down. Anything of significant value I would spend the $$$ and Ship Fed-Ex in my opinion.