Hrqls, KotDB : Well, the dice to go first could be an independant roll. I know that one option in playing (though not on any online site that I know of) is to roll again if you don't want to use the who-goes-first roll. That gives a considerable advantage to the starter.

I imagine that doubles are considered to give too much advantage to the first player on top of being able to go first.

Double 6, 5 and 1 - as you say.
Double 4: Make your opponent's 5-point and your 9-point as you would when moving second (unless there's a blot on your own 5-point in which case you hit it 13/5*(2) with glee).
Double 3: Attack as you suggest, though Gammon-Save would be 13/10(2)  24/21(2)
Double 2: Again attack, 13/11(2)  6/4(2).