I've recently spent some time researching e-commerce solutions for a smaller company in SC. They don't deal with the volume or traffic that you described. Although, I'm definitely interested to hear your solution.
I went through Presto, Magento - installed both to test drive a bit... According to the overall reviews Magento seems to come out ahead of Presto, and my personal experience would concur. Magento may be worth checking out for your use case, their paid plans seems to be tailored for higher traffic stores. In the end I settled with woocommerce as a wordpress plugin... for this client's particular needs it will work best.
HTH and Happy Holidays ya'll...