Un orthodoxly is a term that might not have a lot of synonyms, given its specificity. However, some alternative expressions that can convey a similar meaning are 'in an unconventional manner,' 'in an uncustomary way', or 'in a non-traditional fashion.' Additionally, 'differently,' 'abnormally,' and 'irregularly' can also be used, depending on the context. When writing, it's always a good idea to explore different ways of expressing the same idea, using an appropriate tone and style. These alternatives can help to add variety, clarity, and interest to your writing, making it more engaging and compelling for readers.