I'm a tremendously right-handed guy, but somehow I managed to learn years ago how to play table-tennis with my left hand (I started doing it to level things when I played against friends who didn't know how to play). I would tremendously suffer to learn left-handed tennis. I can't even coordinate a 2HBH since my left hand bothers me, so I naturally hit 1HBH (despite the efforts of one of my childhood coaches who insisted on teaching me a 2HBH without any success). I see that the first problem would be strength on my left side. But I consider that for someone like OP who seems to be "semi-lefty" it is possible to learn left-handed tennis. I think that the most difficult thing would be learning to serve with the left hand!
In any case, I think a 2HBH is almost mandatory for someone who has a useful left hand. And I think learning to use it at any activity is good for the brain. I have an ambidextrous friend (although he prefers to use his left). He knows how to perfectly write with both hands, how to play guitar with both hands, etc. He laughs at me when I'm unable to put a key into a door lock with my left hand...