As a scientist, I would express an uncertain number within a ten-fold range, as either “several” or “the order of”, but never both. As they express the same idea (differing only in the greater precision of “order of”) if both were used one would always be superfluous. So it’s:
“…a period of several thousand days”
“…a period of the order of a thousand days” (British English)
“…a period on the order of a thousand days” (American English)
The latter pair would, I think, sound unnatural outside a technical context.