Would it be possible to change the YouTube embed code? How it is at the moment looks nice and tidy in BBCode, but can be really time consuming and awkward.
If you could find away for the forums to ignore anything before and after the little bit in the address that specifies what video it is - like this-
IGNORE -
http://www.youtube.com/watch?v=
CK62I-4cuSY
IGNORE - &list=UUfAOh2t5DpxVrgS9NQKjC7A&index=1&feature=plcp
then you could just copy your address bar and paste it in. From what I can tell it always uses a "=" before and a "&" after so it might not be so tricky. That way it'd just be two/three clicks to do rather than finding the little bit you want, dragging across it, copying etc.