There are a couple of ways around this objection. First, for reasons we currently have no way of knowing about, Elaine might not have been the only wizard spending time with the Summer Court. Elaine could have met Cowl in Summer and fallen under his influence there. It's possible, but I don't think it's likely. ...
The second and more logical way for Elaine to have met Cowl is before she went to Summer. Cowl could hidden Elaine for a few days and either won Elaine over to his cause through persuasion or nemfected her and the implanted personality within Elaine convinced her to work with Cowl.
Or the 1b possibility, Nemfected Aurora took Elaine with her on trips to the mortal earth and met with Cowl there, perhaps setting her up to be enthralled by him. Just because Harry searched for her after the fire doesn't mean he'd have noticed if she popped out of Faerie occasionally sometimes over the intervening years. He did eventually give up sometime between the fire and Storm Front, assuming she'd died.
Personally though I think it somewhat more probable that Elaine was the vector Nemesis used to get to Aurora. Most likely Cowl was supervising Justin's starborn plan and upon realizing Justin have been incinerated, beat the Wardens to the scene, tracked Elaine down, and took over where Justin left off with the enthrallment. Then he primed her to go to Summer asking asylum and carrying Nemesis with her. I don't think Harry's tracking spells coming up empty is evidence against that - Cowl could almost certainly jam anything teenage Harry could do in that regard. This possibility doesn't even strictly require her to be Kumori, although if Cowl is Simon's secret identity, their master-apprentice relationship helps explain him keeping close tabs perhaps better than just generally being two random associates with nothing more in common than Circle membership.
How much time did Harry have before the Wardens found him? More specifically, exactly how long after Justin's death did the Wardens find Harry and why were they even looking for him or Justin at all? Finally, whose idea was it to send the Wardens out in the first place?
We know he was free for long enough for Bob to tell him to bury the skull and come back for it later if he survived, lest the Wardens capture and destroy him. He could have taught Harry some tracking spells at the time but they failed. I'd guess he was on the lam for perhaps a matter of days, but likely not multiple weeks.
Simon investigating his apprentice' disappearance and calling in the Wardens also fits quite a bit of this.