He's a more than decent fighter - excellent if too impulsive by far, there's no denying that. For the rest... being pushed at the right place at the right time by the Wheel isn't being great, or "accomplishements".

Rand is Rand, and his ta'veren effect is the Wheel pulling him. LTT's memories are LTT's - a massive advantage for Rand, but no accomplishement of his. There's nothing great in the fact vital knowledge from LTT comes to save his butt when he's put himself in a pickle either.

What happens because he is ta'veren doesn't make him a great man. It has saved his butt countless times, when his plans were rash and badly thought out, when he made stupid or immature decisions, usually more out of inexperience and a refusal to listen to advice than by any lack of intelligence. When his luck ran out and we he acted on his own impulses, Rand has gotten himself into massive troubles very often: his great plan to manipulate the two factions of AS ended with him a prisoner. The one time he decided to "be clever" and stupidly tried to control his ta'veren effect, he nearly got killed by Fain. He didn't think things through with Rahvin, and he's been terribly lucky not to lose Mat, Aviendha and his teacher... and that Nynaeve distracted Rahvin at the right moment. His rash decisions in Far Madding landed him captured. If not for Cadsuane, as soon as the Shadow learned that, Rand was a sitting duck for Slayer. His plan for the Seanchan lost him his hand, his plans for the BT resulted in training Darkfriends right under his nose, he nearly unravelled the Pattern to get rid of Graendal, his plans for Sammael nearly ended in total disaster (what Bashere and Mat designed worked as planned, but Rand's part of the plan went badly and it's only thanks to Moridin Rand didn't end up dead) and so on, and so on.

Rand's path is a string of disasters and barely avoided disasters and a few miraculous, most often "Wheel-pulled" successes.

One of Rand's main problems is also that so far he's been a terrible, terrible leader, and he hates listening to advice. By TGS, he's managed to antagonize pretty much all of his allies. The Aiel are turning against him, he's antagonized Logain, Cadsuane and Nynaeve and the AS following him, he's developped an hatred of Egwene and the White Tower out of the blue because Egwene has not seen fit to fall on her knees before him (whereas AS Rand approves of flatter him beyond measure... and turn out to be BA, like Elza and Alviarin), the Tairens and Cairhienins obey him out of fear more than anything.... He let his temper get the better of him and antagonized the Borderlands rulers at a time he couldn't afford to, failed with the Seanchan, abandonned Arad Doman in a state much worse than when he arrived...

Rand sure has the potential to turn all this around and become a great man - he's a great kid caught in impossible situations and yes, he may be doing better than most kids would do in his place - but at the moment he has still a lot of crumbs to eat to become "a great man".

"so there is no way that his mixed gender circle would have been considered 'pathetic by AOL standards.'"

Of course it would have been considered "pathetic", or rather most AS would have soiled their pants at the idea that a newbie at linking would attempt something like this.

Read the scene again. Rand was completely on his own because LTT refused to participate, and Rand came close to bungling it all up for complete lack of experience handling saidar in a mixed gender circle, while Nynaeve barely knew more than how to link. That he waited until the time of the deed to link for the first time, with zero practice beforehand with Nynaeve is typical Rand, and typical rash adolescent behaviour. Rand did not "acccomplish" so much as he managed to get to the end of what he began, and survive - a near miracle. Sure, it was daring and courageous, but that's more immature blindness to danger and the adolescent feeling nothing can happen to him than real, rational courage. Beside, let's not forget Rand planned the Cleansing because of his own big miscalculations about the Asha'man.