I made a terrible, stupid mistake! My Time machine came up full.

To make sure what you posted is clear, are you saying that you dragged folders from an external HD, that are part of a Time Machine backup set to the Trash on your Mac? If that is correct, you effectively corrupted that backup set, and will need to start over again.

Going back to removing those folders from the Trash, then no, there really isn't an "easier" way. You basically have three choices:

1. Wait for them to be deleted.
2. Restart your Mac in Safe Mode, and then, try emptying the Trash again.
3. Use a command in the Terminal app to remove them. Caution: You need to be very careful when using this command, as you could potentially delete things that you really don't want to. If you want to risk it, the command is: sudo rm -rf ~/.Trash/*

Erase the backup disk. The backups it contains can no longer be considered reliable.

They reside on the external hard disk drive, and as you now aware it can take an age for the Finder to delete the potentially millions of tiny files that comprise a backup. Days, perhaps weeks, depending on what you dragged to the Trash, and that's if you don't allow the Mac to sleep or shut down.

And when it eventually finishes... the TM backup will still have been corrupted.