Instead of giving away some quantity at once, why not give away some each day (for instance 1/100 of what you intended) - and the next-days rewards can be depending on the previous trades of the person - if the target is to keep above 0.0001 then anyone who dumped (or tried to dump) below that price would receive only 10% of the initial sum, whoever kept the goal, would receive the same amount. Along with this, there may be also a rule - do not sell at certain price if an offer already exists. Anyone who posts sell offer that repeats the price of existing one would receive less on the next days.
Of course, this can be done only with if the exchange is cooperating by providing data.