What is the process for changing a Non-O visa to a Non-B visa while in Thailand?

Your ability to change depends on a few things.

Are you on the initial 90 day non-O Visa? If you are then you cannot change to non-B without leaving Thailand and either getting a non-B from a nearby Thai embassy, or returning without a visa and applying for a non-B conversion inside Thailand.

Are you on a 1-year extension of stay based on marriage?

If you're on a 1-year extension of stay, then the only time you could possibly switch to work extension would be when your marriage extension is coming up for renewal. Since there's no way to cancel your marriage extension, you would just apply for a different extension reason at the appropriate time. You would need to check with your immigration office first to see if they would allow this though.

If you're on the 1-year extension of stay based on marriage and not near extension time, then you're going to need to leave Thailand without a re-entry permit which will nullify your extension, and then apply for a non-B outside the country or return without a visa and apply for a non-B conversion inside Thailand.

Note that most companies cannot or will not supply the large amount of paperwork required to apply for a non-B conversion inside of Thailand. Most companies send their new employees out of the country to apply for a non-B at a nearby Thai embassy/consulate since it's so much easier.