You can, and it will cost you nothing.
- On the video's mobile Youtube page, tap the menu button at the top left (or right). Scroll to the bottom and switch
to Desktop view.*
- Change the speed controls just like you would on your computer.
- Play the video by tapping it and it will use the new speed settings.
*If you're in YouTube desktop mode but still don't see the gear icon then tap Safari's action/share button and request desktop version from there as well. The request desktop icon looks like a monitor/iMac.
(I recently learned that you can also tap and hold Safari's refresh button to request the desktop version of a page)
If you lock the screen Safari will pause playback, but it can be resumed either from the lock screen or your headset to allow audio only.