Can jazz help my classical playing?

This week I was having an interesting email exchange with a friend of mine who studies jazz guitar.  He wanted to know my take on  comments related to a blog post regarding playing classical guitar vs. jazz guitar...  (paraphrased below)

• Jazz guitarists know the fretboard better than classical guitarists 
• Rhythmic energy and drive is secondary for classical guitarists
• Classical guitarists spend too much time worrying about making the smallest mistake

Hmmm.   From a personal point of view I can confirm I don't know the fretboard at all well and I do indeed memorize a series of shapes and patterns, but my teacher seems to know the fretboard intimately - he often points out that something I'm playing up the fretboard is "just an xyz chord" (news to me!)  And let's face it, rhythmic energy and drive, i.e. a steady down/off beat? is not what's required when connecting musical lines across several measures.  Worrying about the smallest mistake? I figure I'll get to that when I've stopped worrying about the big mistakes. 😆 

But wait!  He followed up with a treatise involving 10 places to play

Cdim/Cm6-5 chords... and 4 (equally confusing) synonyms for the same 4 notes.   What?  I'm not even sure I know how to say that.  I realize that I'm paddling around in the kiddie pool and he's swimming the English channel so far as chords are concerned.  And to be honest,  I don't have much use for 10 places to play a jazz chord just at this minute, but it would be nice to actually have at my finger ends triads etc of major/minor/7th chords all over the neck wouldn't it?  (yes I do know the CAGED shapes and how to use them, but only in theory, i.e. I can work out how to play a C chord at the 8th fret if need be).  So it would be nice to recognize the shapes I'm playing as actual chords instead of having to refer to the sheet music to work out what they are.  The only thing I am confident about in our whole discussion is I can read the exercises (notation) he pointed to without having to convert them to tab!  

So how does this all help me?  I'm not about to start learning jazz guitar - I'm having enough trouble with classical, and anyway I don't have an extra few decades available.  However what I'd really like to be able to do is improvise over basic chords - it's something I'm supposed to be learning but I'm not getting very far, while jazz guitarists can apparently do this in their sleep.  Do I have to know all the scale shapes all over the fretboard and figure out which notes of the scale in the key sig go with which chord and where they are, instantly, on the fly?   Or perhaps just fret all the different chords as they come up and improvise on those?  Or..... well ? you tell me.    Something has not yet clicked, and it's not like I can't hear when it sounds right... the problem is knowing in advance what I need to do to get there!  I'm hoping it's going to be something where I get an aha! moment - like when I found out that modifying the major and minor scale patterns to get the church modes finally made musical sense.  (Previous attempts to understand them had been like peering through the murk at the bottom of the inner harbor).

So enough musing - when I get it I'll post what worked for me (but it could be a while).  In the meantime, here is where I am on my latest classical exercise (where I note the rhythmic accuracy leaves something to be desired still)