On Saturday I installed a different capture card.
It's nearly the same model (different revision level) and using the same device drivers.

Just like the other card, I'm not sure whether the right edge is getting cropped. :(

Sunday I cobbled together a Win98 box from old parts lying about
because I want to try the BT8x8 tweaker program in VirtualDub.
By adjusting HDELAY values in the tweaker program, I could shift the image to the left and actually see the righthand edge.

Yesterday I've recompiled my Linux driver, using the same HDELAY value I got from the tweaker program.
Here's the result: