Big dog could just easily pretend he's 35 different persons all mining at 1% of the net hashrate to avoid the 'tax'.
How would he be able to split up into 35 people. I think he would be spending more money just to avoid a tax.
he would just mine to a new address.
IMO, I think the answer to this problem is egalitarian distribution. Just have to find a way to buffer the payment so you're not just generating dust each time. That way, everyone who is mining gets rewarded.
might disrupt the "rareness" of the coins though.