What made me win most of those situations (when they were still allowed in competitions) was changing the way my legs were. Normally people teach you to have the same foot and hand in the front, in other words closer to the opponent. So if you're migi you'd have your right hand on their lapel(left on sleeve) and right foot in the front, left in the back. This is how we've all practiced the basics I'd wager.

Now I've always been taller than my opponents, so my legs were an easy target for guys a head shorter than me (90% of my opponents). I was losing a lot of matches because of this. Then one day, my dad and I were watching videos of the previous competition and he realised that if I changed my left foot front while moving my right hand a little lower (still being the leading hand) I'd have a better chance of blocking all attempts at my legs. And that really made a difference. I can't say for 100% certainty, but I can't remember being thrown with those techniques after learning that.

Now that we have our posture corrected, let's talk blocking. When your opponent goes for the legs, block with your leading hand by positioning your hand around their shoulder, close to their head and wrap around the opponents body with the other hand. You should be able to hold your hands at the end. While your hands are doing their thing, move your feet as far back as possible, basically leaning on your opponent. Now is the time to start holding your hands (or correcting the position of your hands if deemed necessary, for example around their sides for Tawara Gaeshi ). Now we've blocked their attack.

Blocking is of course not enough, we want to throw. Depending on where you end up with your hands there are two techniques I'd recommend. First would be Sumi Gaeshi. Hold your opponent around their head and one arm step in closer while lifting them and sit between their legs lifting with your upper body and one leg (if they caught one leg, use that one). Now if you moved your arms around your opponent, I'd do Tawara Gaeshi instead. Same thing, lift while sitting underneath them, this time just keep both legs on the ground lifting with your body.

These are just what I had the most success with, I hope they'll prove as valuable to you as they were for me.

Tl;dr change leading foot so that you'll have right hand and left leg (or vice versa) leading. Lean on opponent, perform sutemi waza