There are a few reasons why execution is so expensive, which can all be solved.

1. The drug, which is not only expensive, but can take quite some time to acquire (since drug companies don't want to be seen as killing people). This can be solved by changing to a cheaper and more available method.

2. Jury selection, which can be streamlined by electing a pool of qualified jurors to be randomly selected. (This is my solution to ignorant and biased juries, but can apply here as well.)

3. The case is bounced around different courts until reaching a federal judge. This issue can be solved by requiring death penalty cases to immediately go to state supreme courts, and only allowing appeals to SCOTUS for reason of unconstitutionality.

4. Bloated salaries for politicians (Judges are politicians, even on SCOTUS, which has become a third house of Congress). This can be solved by fixing their salaries to the median income (which is my solution for their inaction towards poverty, but can apply here as well).

5. The largest cost is the time on death row. This time can be drastically cut by implementing the above reforms, and putting in place a legal requirement that executions be carried out as soon as possible, once all trials and appeals are done.

The chances of convicting an innocent person go down once we democratize the juries, and over time as technology advances. I'd be open to increasing the evidence requirements for a death penalty conviction, as well.

The death penalty is a necessary evil to keep society safe. Once they're in hell, they can never commit a crime ever again. The only way to make the process more accurate and less expensive is to innovate.

The most important thing to do is remove the need for the death penalty in the first place: we need more access to mental healthcare, and less children being born to dysfunctional families or with mental defects. I can elaborate, but to prevent this from becoming an essay I'll end it here.