Can I apply for a new non-immigrant B visa online while still in Thailand?

You can apply before the last Admitted to Stay date for an 1 year Extension of Stay based on being employed in Thailand at your local Immigration Office.

You can not apply on-line for a new visa while residing in Thailand.

you have to upload your passport pages when you apply for the eVisa online and it will show you don't have an exit stamp for the current entry you're on in thailand

AND

You have to show that you're flying out of your country coming here (which won't be a problem if you're going back to the US)

You would have to select the US as your passport and your place of permanent residence or the system won't let you proceed too.

All you can do is apply and see if it goes thru or if they email you