First of all, the question posed in the OP was what would you do whether you were Israel's PM. That means that all you have right now is the IDF and possibly some US forces, though I don't exactly know whether they may be commanded in the same way. So the question is, what practical strategy do you have in mind given the capabilities and limitations of the IDF?
Let me put it another way: how do you "weed out" some 30-40k Hamas agents (with thousands more inactive supporters) from a densely populated urban area, while simultaneously defending your country from airstrikes from two borders? Do you have soldiers knocking on every door in Gaza and politely asking whether there are Hamas agents there?
Here is what the IDF has been doing so far: Pushing Gaza civilians to move to the southern part of the strip. Hamas has blocked these efforts but several hundreds of thousands still managed to evacuate. Then the IDF started bombing northern Gaza, attempting as much as possible to concentrate their strikes on particularly locations they knew, per military intelligence, to be housing Hamas cells, weapons and supplies. As in every war ever, some of the casualties included civilians, people who did not or could not evacuate. We've now reached the second phase, which is the ground assault.
Given all of this, what would have been your practical strategy to "weed out" Hamas, which you have hinted to being superior to the IDF's strategy? In case you might be wondering, I am honestly curious and not being sarcastic. Though I served in the army, I'm not a military strategist.