Hi awer1,
Remote diagnostic and repair of bicycles is never easy, especially for the kind of difficult problem that has already been examined by live mechanics.
What I suggest is to unscrew the low-limit screw of the FD so that the FD goes a bit further inboard than you think is best. That should increase downshifting performance at the risk of increasing the risk of dropping the chain inboard of the inner chainring. Also, make sure your bar-end shifter allows the cable to become completely slack when the shifter is all the way down.
If it works, you can deal with and stop all chain dropping with a chain guide like the
N-Gear Jump Stop.
Don't worry, such an adjustment is very safe once you have a chain guide.