There is no evidence that Yuya had been thrown in jail. The Arabic document merely confirms that this vizier had been alienated from his king, only to be reinstated and elevated at a later stage. This matches Joseph's fall from grace and his later appointment as a high profile figure in Egypt. Yuya must therefore have had a run-in with either Tuthmose IV or his son, Amenhotep III.
Getting past the fact that I don't use the American Standardized Version but the King James Version, which doesn't say "comely", the word "comely" as in "attractive" isn't quite on par with "exceptional beauty".
With no evidence that Yuya had been thrown in Jail nor that he lost favor with the king or his son and was later reinstated there's nothing to support your contention. Because you want it to be true doesn't make it true.