Chase888 in post #36 mentioned the QF HS125. Perhaps the larger airlines which fly the 777/747/A330/A380 ultra longhaul sectors, could afford to provide a programme of manual flying of small jets for their long-haul pilots, and some jet flying exposure for the chaps who "don't need flying skills". But they won't do it voluntarily, and such a proposal wouldn't be viable at all for small carriers.
SIA used to have a fleet of Lear 31s for just this purpose. Not sure if they still have them though and, if they don't, would be interested to know why the programme wasn't deemed useful enough to continue. Anyone know?