The aftermarket shifter is the problem with that Brompton fold, you can see it in photos 13/19 and 6/19. Brompton bars are well centered around the front wheel when folded and should have plenty of clearance for bar-ends, esp the S.

The cable exiting the shifter runs foul of the steering tube - he already has it set as far as it can go with the cable touching steering tube. Then the shifter box is also rather thick so it forces the brake lever/housing to a bad angle that then runs foul of the fork when you fold it - you can see paint chip marks on the fork where the brake cable screw adjuster is contacting it. Not sure if you can run the shifter cable on the other side of the steering tube - Brompton's stock cables tolerances are quite tight... but *maybe* swapping in longer M or H bar shifter cable might do it.

I'm a Brompton convert, personally I consider the rack (and its ability to easily roll while folded in shopping-cart/carry-on-luggage modes) to be one of four critical attributes that sets this bike apart from any other folder - the other three being: fast fold, small fold, and luggage integration (riding AND folded).