The problem with requiring someone to hold onto shares for a specific amount of time is that it doesn't prevent HFT but instead adds a barrier to entry. If I buy 5 shares of IBM but then must wait a week before I can sell those 5 shares what prevents me from selling these other 5 shares I bought last week? If there was a company that held several stocks that were readily trade able other people could contract selling the shares & replacing them for a nominal fee. This would be similar to shorting stocks.
One possible solution would be to trade shares on a fixed schedule, ex: every minute but not between minutes. This would provide everyone the same amount of time to react to the information. The difficult part would be deciding between who wins the bids, since time is an unfair determining factor that leaves some other metric like price bid or bidder's history or a random element.