And I have just the solution:
One of the problems I have w/ corkscrews is getting them started evenly/straight into the cork. The tip comes in at an angle of the screw, so you have to start it w/ a small offset towards the side to drive it into the cork straight.
The original plastic ScrewPull seems to be the best corkscrew for driving the corkscrew in straight. You just hold the two prongs tight against the lip & start twisting. My new ChefMan electric corkscrew has enough play (so it can deal w/ wide-lipped btls like Turley) that it often starts into to cork at a cockeyed angle & makes the corkscrew struggle as the cork rubs against the side of the barrel.

So my solution: Instead of the corkscrew tip coming in at an angle, why can't you modify the tip w/ a slight offset and a short (maybe 1/4th ") straight/vertical segment that aligns perfectly w/ the axis of the center of the screw?? Does that make sense, if you understand what I'm getting at? A drawing would probably help to explain.
I've never seen a corkscrew screw that looks like that. And it would probably increase the production cost to add that little fillip to the end of the screw.
Whose with me on leaning on the corkscrew manufacturers?? I'll be glad to lead the charge.