Can I apply for a Non-B visa based on my work contract while on a Thai wife visa, and will it count towards residency?

in addition to your contract you show that you are paying thai social security (it's a certain form number) and you show the company documents that lists the thais employed to offset your foreign employment, your bank book, and the work permit.

It's a PILE of documents and if you have an extension comin' up in a couple three months you need to go over to the immigration office OR have your HR dept go and get the requirements as far as documentation to apply for a yearly extension based on marriage using employment inside the country

Concerning residency you're getting the cart WAY before the horse on this. My advice is make it thru a couple years of unbroken extensions FIRST before you start thinking about anything else.