One of the reasons they made March 31st World Backup Day is to prevent data loss in case of a nasty prank on April Fools' Day. Not sure how realistic a threat that is, but it sort of defeats the stated purpose of World Backup Day if your backup won't complete until mid-May.
Also, most remote backup services allow you to restore files and folders selectively, so you just need to download a small amount if you're in a real hurry.
One option that Backblaze (and some others) offer is the ability to order an external hard drive with all your data via FedEx. That way, if you need a terabyte of data back, you get it quickly.