from https://docs.generic-mapping-tools.org/latest/gmt.html#r-full
For calendar time coordinates you may either give (a) relative time (relative to the selected TIME_EPOCH and in the selected TIME_UNIT; append t to -JX|x)
Then I think that
-R110/280/373420800/381369600 -JX10cd/10ct --TIME_UNIT=s --TIME_EPOCH=1970-01-01T00:00:00
should have worked.