To anyone with the means to do so, might even be worth a holiday to Nova Scotia to hand in the application in person.
Otherwise to Canada from anywhere but the US will likely take at least a week and you're at the mercy of the courier to get it delivered.
We didn't do that when we applied, but then the caps were 1000 back then.
I think the computer programmers will be one of the first to reach the 300 cap. In the entire world it's conceivable there's already 300 with their documents in order just waiting to mail to CIC.
Failing an in-person trip I'd certainly look into getting the application mailed to CIC with instructions to the courier to deliver ON 4th May, and send it well in advance. I'd think some couriers may have an option to hold at the local depot for a number of days and then deliver on a specific day.
Best of luck to you all!
Wayne.