First of all, if you are getting cold sores that often, there is something off with your immune system. Pay attention to your pH (which is affected by diet, exercise, and strong emotions.) Once I started paying attention to my pH, I greatly reduced the number of outbreaks I get. Maybe once a year now.
When I do get it, I am eager for it to go away, so like you I have picked at the sores and tried to apply whatever topical solution I was using at the time directly to the sore. I have had some success with this at catching it early and reducing the scabbing and overall healing by a few days. But basically once it has erupted you still have to go through that.
Always better to stop it before it erupts. A lot of the time I can feel the conditions that bring it on - excess acidity causing fatigue, and sometimes a tingle in my upper lip - and take steps to bring my body back to balance before an eruption.