If you're falling a lot you should think about some bike handling exercises. Low speed maneuvers will likely help. And when you hit rough ground, relax. Twitching the bike while in gravel will just make you go down faster. Just relax, hold on and pray for traction to improve before you reach the point of no return. I've avoided my worst accidents that way. One in particular flummoxed the guy I was riding with. He didn't say anything for a full minute after. That was, uh, quite a recovery (If I'd gone down it would have been a five man pile-up, probably with him at the front of it).
I haven't ridden seriously for years but my partner thinks I'm crazy for driving one handed. I had lots of practice doing low-speed maneuvers one-handed (end of the ride, it's hot, I'm thirsty). I could emergency brake one handed (once dual pivot brakes existed) For a brief moment I could do a track stand one handed. Driving one handed I'm more stable than most people are with two (also, grew up driving stick, so one-handed is de facto if not de rigeur).
I don't know if they still do this, but pros used to wear silk shirts under their jerseys to reduce road rash (source: Phil Liggett). I suspect any current gen synthetic sports undershirt (under armor, Kuhl, DSG, etc) would do. Two smooth layers of clothing will spin past each other instead of gouging you.