The acid is there to help with keeping everything emulsified. You can do away with it if you emulsify carefully, and will get a creamier end product. Also, the oil matters. Try making a batch without any citrus or vinegar, and then try a couple different oils. You'll find one that works for you, I'm sure.
As for yolks/whites, I use both just because I want to use the whole egg, but I've had good creamy mayos made with just whites, so that may be something to try as well.
Cooking on a crazy contraption...