Can I extend my 3-month Non-O visa for one month while applying for a 1-year Marriage visa?

You should already be on a marriage Non-O Visa and you will be looking at seasoning your funds for 2 months then applying for a 12 month Extension of Stay, not a Visa. The Kor Ror 22 can be obtained in minutes at your local amphur so I assume your constraint is the seasoned funds unless you were married outside Thailand which means you have not planned this at all well.

All extensions regardless of length are 1,900 baht.

You can apply for a 60 day extension based on visiting Thai family. Also you would be able to then convert to a marriage extension from that.

Ask your local immigration office for their handouts of requirements needed for both.