Can I use a 1x10 wide range cassette with Shimano SL-BS79 bar end shifters?
One thing you could do is use a Microshift Advent 9 rear derailleur. You could even get the clutch one. They're 9-speed Shimano compatible, which means they use the same actuation ratio expected by a 10-speed road shifter - there are many questions here about this. The Microshift mountain compatible bar ends are another path, but having worked on tons of bikes with them, I just don't like them all that much - the lever motion is sloppy and indeterminate, especially compared to the Shimano one you've got, plus you're buying an RD anyway.