I live in the northeastern U.S., am a native English speaker, and I have used both in this context. They are entirely interchangeable as transition words.

"Further, I have found that writing papers gets boring if I don't use varied transition words."

"Furthermore, I have found that writing papers gets boring if I don't use varied transition words."

I have used this in my various college-level English courses (it's my minor) and no professor has ever commented, even when I use both in the same paper. "Furthermore" klingt ein bisschen mehr "wissenschaftlich", aber nicht veraltet.

Auch, andrOgene hat Rechts, "further" bedeutet auch "weiter". Wann es ist so dann ist "furthermore" nicht mehr gleich mit "further".