Quote Originally Posted by Lumens View Post
I know a better lens ("L") or Full Frame might resolve my issues
Not a completely accurate statement.
A faster lens or a camera that handles noise a bit better will help you go longer in the field before you lose light. With the best gear you might gain 4 (+/- 1) stops of light. For your 300mm length those stops will come with a price tag of about $3000 per stop.
As evening falls no equipment short of bringing your own lighting will resolve the issue.