Can I convert a single-entry Non-O E-visa to a normal Non-O visa without leaving Thailand?

You cannot "convert" to a normal non-e-visa. You are talking about applying for an extension based on your visa. E-visa or not makes no difference to the process.

If you left before you could apply for an extension, that means you will have to start over from the beginning by getting a new non-O visa. You'll either need to leave Thailand and apply at a Thai embassy for a new visa, or if you qualify, you can apply to convert to a non-O visa at your local immigration office. This will require you to have money in your bank account or proof of income verification from your embassy if they offer this service. You need to go to your immigration office and ask them for their list of requirements to convert to non-O visa based on whatever reason you are seeking, whether it's retirement, marriage, supporting Thai child or whatever. Each immigration sets their own requirements so you need to go to YOUR immigration office and ask them for this list. Then you will know what you need to gather in order to apply to convert to the non-O visa. You'll also need to have a certain amount of time remaining on your entry stamp in order to apply, but how long also varies by immigration office.