For the DNA I made, I imported pdb data and generated curves from there, but I'm not suggesting you do that. Probably overkill for a logo.

But for accurate DNA, I do recommend you make sure the helix is right-handed (Make a thumbs up sign with your right hand and follow the helix in the direction of your thumb; your fingers should curve in the direction of the spiral. The helix you have made in post 5 is indeed right-handed) Also beneficial to incorporate a major and minor groove, instead of perfectly offset helices.