I have gotten a headache trying to follow OP's logic.
First, if I understand it all, OP is willing to give up a claim for $375k ($250k to OP, $125k to lawyer) in favor of taking a matter to trial his/herself.
OP, you do understand that one of the many benefits of mediation is certainty of payment? If you go to trial, and get a judgment (which of course may or may not happen), there is a whole other set of hurdles?
First, the other side might appeal. Not only will that mean additional YEARS as the appeal winds its way through the legal system, but you will have to pay for appellate lawyers. By the way, I have yet to meet a single appellate lawyer who works on contingency. The cost of an appeal is not included in the contingency fee you are paying your current lawyer. You will have to pay appellate lawyers out-of-pocket for (expensive) appellate fees. In most cases, appellate fees are not recoverable (since we don't know what kind of case you have, I can't say with certainty if they are or not). The appeal may be successful, which means you are back at square one.
Second, if you do get a judgment and prevail against the inevitable appeal, or there in no appeal, you now have to collect the judgment. Is the other side credit worthy? Are there assets? Will there be a bankruptcy? You do know the low percentage of judgments that are successfully collected, right?
Thus, you need to realistically weigh your mediation offer - which comes with it the certainty of payment - against the issues raised by appealing and collecting a judgment. This is worth a significant discount over what a trial judgment might be. The mediator knows this, and thus valued the mediation settlement considering this factor.
You have been given excellent advice on why to accept this offer, and why you are being unreasonable to insist on going to trial. I won't repeat all that, as you have obviously want to simply ignore the logic that has been expressed.
You need to reconsider your decision.