I'm not sure if there is an actual non hacky way to do this, but the last time I remember someone doing this was back before 1.0 and he basically either 1. made people mine the block several times or 2. cancelled the playerinteractevent until they attempted it a set amount of times. Again, both very hacky ways, might be really easy by now
I need to do this for individual blocks. For example, some grass blocks need the modified strength and others don't.
Do you want it to be slower or faster? For slower, you can add the Mining fatigue potion effect. For faster you can use Haste. http://www.minecraftwiki.net/wiki/Potion_effects