I've heard and seen people do the "running start and bump" with the starter, but it never works for me, I almost always slip off to the side.

I put the starter against the nose and hit the switch. But I do rotate the prop backwards against compression to give the starter a running shot at the compression stroke.

And you are correct, you don't usually want the cone pressing on the prop. Though there are some cones made by Sullivan designed to grab the prop. Never used them myself though.

I do find that the dubro spinner nuts are big enough in diameter to work with most normal starter cones, though they don't look very scale.