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.
If this is a problem of scarcity, then why not just make a coin that gives a random number of coins per block. Maybe between 1-100.
This coin won't fluctuate like the others, making it stable and easier for investors to get their money hungry hands on it.