Absolutely do not apply in Malaysia. They are very strict and you have a high chance of being rejected. It will also take more than a month to process. Most people are going to Vietnam lately. 1-2 weeks.
Why don't you apply in Australia before traveling though?
Not sure where you're getting your information, but you're way off on a lot of things.
First of all, there is no 30 day entry. If you entered without a visa then you received 60 days.
Next, bank statements don't mean anything. If you want to apply for a non-O you only have 2 options. Proof of 800,000 in your Thai bank account, or income verification from your embassy in Thailand. It appears you are from the US, and the US embassy does not offer this, so that means your ONLY option is 800,000 baht in your Thai bank account. You do not have any other options for the non-O visa, or the first 1-year extension.
Finally, there is no insurance requirement for a non-O visa or the extension based on a non-O visa. Whether or not you need a lease is up to your immigration office. Some might require and some will not.
Thai citizens line is not the same as fast track line. Also neither of those is the same as "safe entry" fast track which is a guaranteed entry through an agent.
One of the requirements to enter Thailand as a tourist is proof of onward travel. Though it's rare to be asked, you can be asked for proof of your ticket out of Thailand.
There are 77 provinces in Thailand, and each one has their own immigration office. Each of those offices has their own policies. That's why I said that some office allow it and some do not.
Why are you assuming this is someone's very first trip to Thailand? Some people have been traveling to Thailand for years or decades, and have bank accounts from the past.
Then go to your immigration office after you arrive, ask them for their handout of requirements to convert to non-O visa. Then gather everything on the list and return to apply.