gear inches matters, but it just means that the heavier the gearing the more committed you have to be. heavy gearing will want to kick you more, but you can lock it up just as easy if you are forward enough.
Bullhorns will help a LOT. You can get forward another 6 inches or so.
Small gearing will help makes things a bit easier for now, even if that sounds like a contradiction to what I just typed.
Vittoria Randonneur tyres skid like crazy, and are strong and cheap.
A bigger frame that fits will help a lot too, because the bars will not hit your knees.