I am an absolute FIRM believer that the hand you write with, should also be your picking hand on the guitar.
I am right handed, but I am a very ambidexterious righty......but I could not imagine my left hand doing the picking.... and I don't see how a lefty picks with the right hand.
I can play a left hand guitar somewhat......but the "somewhat" part may surprise you... I can do fast hammer on/pull off legato, and patterns fairly clean with my right fretting hand (when playing a left handed guitar) , but my left (picking hand is lost and confused).
Luckily all my guitars are for the right handed me.
But if you write left handed, and you play right handed, and you have been "stuck" in the intermediate level for awhile.... strongly consider getting a left handed guitar where your dominant hand does the picking.
If you see the Joe Walsh "Star Licks Video"(Walsh is a righty player) , he tells GIT instructor Tom Kolb "Everyone thinks this hand is so special (holds up his left hand) , hell, anyone can do this fretting part" "Right here is what determines whether you can actually play or not (holds up his right "picking hand").
I agree 100%.