I am lefty that played now for a year lefthanded. Strumming was never precise enough and fretting was slow. I took a righthanded guitar and strumming was ok but my righthand need a lot of practice. My left hand does all the chords without any problem, the F chord goes with no problem, barre chords goes natural. As I want to learn jazz guitar do I get in trouble with my right hand or go back to lefty?
It worked for Jimi !! Being left-handed, your L.H. fingers are probably more 'dextrous' than the other hand's.So fret wise, you're going to be o.k., as you've already found. Strumming is an arm movement more than a finger movement, so your right arm should cope. However, with jazz, you may well find yourself not strumming as you would for, say, a pop song.There will be more 3 or 4 note clusters, which can be played more like picking.Soloing will obviously be by picking, either with fingers and/or pick. This done with your 'bad' hand may be trickier, but I think it's worth the effort.
You're at a gig, and someone offers their guitar to you for an impromptu number."I wish I could, but I only play lefty" will leave you frustrated.Of course, you could always do what Hendrix did - learn to play both ways !