I saw that, too, but thought her price wouldn't allow her to do so, or realize it.

Her price doesn't let her realize that she knew/loved Syaoran in the past. It never stops her from falling in love with him post-payment, though.

Sakura only had one price-related fainting spell in the manga, and that was when she was on the verge of figuring out that Syaoran must have known and cared about her before she "met" him in the first country. Then she immediately passed out and forgot about her revelation. This was in... whatever that VR version of Taisho-era Japan was called. And after that point, the narrative kind of completely dropped the whole "Sakura getting her memories back but without Syaoran" angle completely.