Sounds like a dream having customers scooping up your products the millisecond the appear on the website. They should increase their prices.
No matter what the price, they would still have the "As stated before the main reason we needed to block it was volume of the traffic" problem that was stated above, for a popular item. In fact increasing the base price might attract even more scalpers and such.
Because you presumably want real, returning customers, and that means those customers need to get a chance at buying those products, instead of them being scooped up by a scalper the millisecond they appear on the website.