You can't avoid the fact that if you want to make your muscles stronger they have to get bigger, what I would do is concentrate on climbing muscle groups with the method I mention, and then maybe take it easier with other muscle groups (particularly chest and legs) but still train them to a lesser extent to avoid any major imbalances.
There is science to back up the methods I mentioned before, not just my big arms, but I've long forgotten it, and you could do 5 sets instead of four, but you should be too tired after the third and fourth to be able to, in which case you are no longer training strength and power.
Get crushing!