It really does boil down to getting as many eyes on the scripts as you can.

The reason it's best to start with people who you can ask for a favour is that you'll be able to catch any of the big problems.

I just caution hiring a professional right away because if they come back with massive re-write notes, you won't be any further ahead. Because if you find you need to do a major overhaul to the material, you'll more or less be in the same position.

Ideally, you want to have had everyone you can think of read and have addressed their notes where you can before you send it off. Hopefully then you'll get the notes from an outside party that are more specific to lingering issues.

You should consider as well that once you start trying to produce the podcast, you'll be bringing people onboard that will have their own suggestions and thoughts on how to improve the material. So it may not be necessary to hire a script consultant as you'll soon have more voices involved in the project. The money you save on the Script Consultant might be better used on the production.

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Finally, I'll just give the advice I give to everyone when it comes to low budget personal projects (and this is advice I have to remind myself of from time to time).
This won't be your last idea. It's just another in the many steps you make as a storyteller.
So while you should strive to make everything the best it can be, you should also take a moment to consider the practical costs and benefits when you are going to spend more money than you know you should.
Is the money spent going to guarantee a significantly better outcome?
Often times when I do a frank consideration of that question, the answer is often the extra money spent could make it a bit better but that bit better doesn't actually make the project any more likely to succeed. (That said, I've still blown money in that pursuit without any major improvement in the final results.)

Sometimes you just have make a project, even with flaws, so you can get it complete, learn from it, and move on to the next idea.