I have a feeling you've never spent a significant amount of time dealing with IP and patent attorneys.
You can't threaten to sue. That can backfire in a major way, having lawsuits filed against you.
The idea of reaching big settlements with minimal expenditure's does not align with reality. This simply don't work that way, particularly if you are up against a large or well-funded company.
The first thing an attorney is going to ask for is a retainer somewhere in the range of $100K to $250K to get started. Whatever they ask for, they are likely to tell you they will not move forward unless you can commit to $250K at a minimum to pursue a case.
They don't do this because they are greedy, they do it because this is expensive and they don't want you to burn through $100K and then discover you'll need more, don't have it and you got nothing for your $100K.
Selling IP is an entirely different conversation. Yes, patents can be worth millions, tens of millions, even without a real product behind them.