Once you put him "On Notice" that there is a potentially chronic issue - he has an obligation to resolve this issue.
GET THE ENGINEER! Good luck - don't let the builder push you....
If you not convinced the problem has been corrected, and are nervous to close, you may find it worth a call to an attorney. The attorney can review your contract and provide you advice.
The terms of the warranty would dictate what is covered.
You will want to know what your post closing protections are. Maybe a local TX agent will be able to shed some light on that, but it might really need a review of your specific documents.....and your best source for contract review is an attorney.
I would like to have the builder resolve the issue but I am not sure what leverage I can use to make that happen. I have already paid about 25K in initial payments (half the upgrade cost).
Do I just boldly tell the builder that I can not close until the issue is resolved? They bring their legal weight on me - which I am not able to react to.
In fact you may want to ask the builder to find a licensed structural engineer who will inspect (at their cost) and provide an opinion letter with his "raised" seal. Once you close and take ownership you have little or no bargaining power.
This could be a serious and ongoing problem. It is better to get it resolved now - before you own the property - then go to settlement and be stuck with a cronic problem.
Structural engineers usually are licensed. Check with the state to find some that are local - then select the one with the best experience with this problem to assist.
They will know how to best document this problem.
You are in a good position - as you have not yet settled on the home, and I am sure the builder is anxious for the home to go to settlement. See if they will sign a document guaranteeing the repair.
If your expert is not confident that the French Drain will solve the problem - you should think twice about settling. Be sure the expert you hired is competent with a good reputation. You may need them to testify should the builder sue for not performance.