I would like to award 1 point to each team for the draw, then play golden point/extra time for the 2nd league point.

You mean like having a losing bonus point, that's being discussed previously on here.
The other problem I see with additional time is injuries, with the onset of fatigue the match could easily go on for another 10 minutes, the players are shattered already and injuries are more likely.
Keep it at 1 point apiece IMO

I imagine this has already been mooted and Sky kyboshed the idea. It has the potential to cause scheduling problems for them with no tangible benefits to anyone

The problem with this though is a team could finish top without winning a game within the 80mins,highly unlikely but possible.

There's nothing wrong with a drawn game. It's often a fair result.

I would prefer to keep the draw, fighting back to snatch a draw makes for great entertainment. We don't need an extra 10 mins or so attempting to force a result.