I don't see a really compelling reason for you to do this, other than you think you should be doing it.
Leicas, or rangerfinders in general, are great for most shooting (and especially street) because they're quiet, fast (once you know their benefits and how to use them) and smaller than most SLR's.
I went from Nikons (which I still have and use once in a while) to a Leica because I knew I'd be shooting a lot more street and watned something smaller, a bit less obtrusive and quiet. I also wanted something smaller and lighter for general 35mm shooting and something I could conceivably have the rest of my life.
I find I focus quicker with SLR's, but zone focusing is used mostly with my Leica anyway. I also find I approach shooting differently with a rangefinder...perhaps a personal, subjective thing but it's a bit slower and more contemplative, perhaps. Being able to see outside the area I'm recording on film is interesting for being able to 'pre visualize' my shot as it happens, I suppose.
If you think something is lacking or is a bit frustrating about your street work now, then maybe look at a rangefinder. But otherwise...keep at it with an F6, a fine camera. I find the advantages with a Leica mostly are quietness and unobtrusiveness.