I'd've been surprised if you had. It's all word salad. That's what happens when people start seriously arguing that 'belief' and 'knowledge' and 'true', etc... actually have clearcut meanings.
Sorry, but no. It doesn't help. (I don't even know what fact you're talking about.)
The silly part of the definition is the 'true' part. According to the definition, we can only have knowledge of a thing if the thing is true. I laugh hysterically every time I hear that. It guts the entire definition with one deft move.
Jesus rose from the dead and Joseph Smith found golden tablets and many gurus walk on water and I can talk to my dead grandmother.
I know all these things because they are justified true beliefs.
In other words, everything is knowledge. All we have to do is justifiably believe that the thing is true.
Talk about a definition swallowing its tail!
I have the same problem with the "justified true belief" definition of knowledge. It's impossible to use.
That's why I tend to just go with how people actually do utilize the words knowledge and belief. There is definitely overlap between the two; the usage isn't even clear cut. But generally, people use words like "knowledge" and "I know" when they are talking about something they believe to be certain; it is a belief without doubt.
Belief can be used to mean the same thing, of course, but it also has the ability to refer to things we hold to be true without being sure about.
(Though I know that even this approach probably won't satisfy you since you like your ambigosity. )