I think we would need to develop a system that restricts the potential jurors to those who are qualified without restricting it so much that they are drawn from a small set of gatekeepers who can easily be corrupted.
Perhaps both lawyers could be allowed to negotiate requirements for the jurors (e.g. they must have a technical background, at least half must have college degrees, etc.). Or perhaps each lawyer negotiates requirements for some of the jurors with the judge.
Another approach would be to make changes to the legal system. For example:
Make it illegal for a lawyer to present evidence that they know to be scientifically or technologically unsound or to present a witness that they know to be unqualified.
Make it perjury for an expert witness to knowingly present scientifically unsound statements or to comment on something that they are unqualified for.
Make unsound science valid grounds for overturning or appealing a case.
Require statements to be backed by data that meets statistical requirements.
I'm not a lawyer and I'm sure these wouldn't be a perfect solution, but perhaps they would help.