I just bought an H type Brompton for my girlfriend since the M type was out of stock. I bought an S Type flat handlebar to reduce the height and I have a couple of questions.

Roughly how much should I cut off the cables?
Is the handlebar sweep back or sweep forwards?

You could use info from the German Bromptonauten forum. Here is a thread with an S-bar on an H stem. This thread gives handlebar height and elevation for different stem-handlebar combinations, which helps estimate the cable shortening. Use a web translator. I would start riding first without cable shortening to check whether the expectations are met.