My Amiga to SCART cable works fine with my SCART to HDMI box. I have no reason to suspect it, but I know there can be differences in the way the cables are made.
A/V mode switch or 4:3, 16:9 selector is not part of hdmi, hence box is working with your cable, but composite converter not.
I don't think sync is a problem as that signal has been decoded successfully in your hdmi converter. Without you wouldn't get a satisfying picture on screen.
Addendum: To my knowledge, a tv or monitor built with pal/ntsc tv interface can handle 256 (240) line mode (512/480 i). That is part of the specifications. Modern gfx cards and some Monitors no longer deal with image date lower than 640*480 (31kHz). Output has to be doubled to be accepted (upscaling, frequency doubling).
Using interlace doesn't change a thing, as signal remains the same (15kHz).
You need Multiscan or DoubleNTSC mode to check. They are in the 30kHz ballpark. Those aren't RGB PAL/NTSC conformant and none of the gaming consoles from good old days uses other than low freq tv out. That's what the converter is made for.