The phrase “to the queen’s taste” means: to a fare-you-well; lock, stock, and barrel; completely; utterly; totally.
There was no individual queen to whom this phrase alluded, but because a queen is the highest lady in the land, all virtues are ascribed to her, including possession of all that is complete and thorough.
Curiously enough, the expression is American.
It first appeared in William Harben’s Abner Daniel (1902): “You worked ‘im to a queen’s taste, as fine as spilt milk.”