Dippy eggs are the best! I still call them dippy eggs, even though my kids are grown up now.
You said you can't stand the whites...I can't stand the chalazae... that white stringy stuff. I ALWAYS take it off when I make eggs unless it's a boiled egg and I can't crack the shell. I make a lot of poached and baked eggs and I crack them into a small strainer, drain off excess, liquid-y whites and remove the chalazae the best I can, without breaking the yolk. I also do this if I'm making a Hollandaise. I think I have an egg problem.....

They actually do cook better without the extra liquid-y white.