Really, forget about trying to through your "attackers" and focus on just moving off the line and keeping your center line unified. Keep Hamni as Aikido was intended, instead of taking a traditional fighting stance like you would in TKD. As they attack, don't dance around, sink center and enter off the line. Try to get to their side and behind them. Of course you need to keep your hands extended in front of you to protect your face, head, and torso. Get to this position, first, and see how they react. If you try to just grab a limb and start twisting, you aren't doing Aikido anymore.
Maybe in a more TKD context: You have someone punch at you, as you block step into the arm, not the punch, but the crook at the elbow with your block extended to protect your head. Punch in like a hook motion toward his face and hit him where the head of the bicep is just above the elbow crook. Step through under the arm and pivot so you are now facing the same direction as he. Your blocking hand now can grab his punching arm at the elbow, not the wrist or fist. Now you can kick his leg out from under him, hit him in the back of his ear, or wait for him to decide to turn and face you. Most likely he will almost instantly turn to face you, as most humans would rather not have someone they are fighting behind them. This is where you find out what technique you will use. Typically, I find barring the affected arm is best right after striking it and stepping through, as the typical response to this is for him to bend his arm. There he just gave you sankyo. You didn't have to try and twist his arm up for it. If he keeps it straight and tries to push into you at the arm bar, then you have nikyo. If he attempts to both push into it you and turn you can start irimi nage, or kote gaeshi.
It won't go this clean the first few times you try this, but that's why you train. I used to have some of my neighbor kids come over once or twice a month, and we had basically a randori session in a room I converted into a home dojo. They jumped at the opportunity to get to fight one another on the mats as pretty much any high school or college kid will. Now you will say, they aren't trained fighters, and you will be correct. What this type of experience will do, is get you out of the 1,2,3 mode of performing your technique.
People who train for self defense, don't train to fight professionals. In Aikido, we try not to fight at all. That's where the no competition aspect comes in. If you go into a confrontation thinking of beating someone, you have engaged in a competition where you can lose. If choose to merely protect yourself, instead of beat the other person, you change the dynamic of the confrontation. Isn't that some of the premise behind modern MMA. If the guy you are fighting is a better striker than you, you don't try to stand up with him. If he's better on the ground, you try to keep him standing. So why would someone want to fight, a professional fighter if they are not one. Again I assert I have not read the overwhelming accounts of rained professional fighters assaulting people at random. That point of view is based in fantasy and what-ifs.