LSL6 and LSL7 I've got working, as well as KQ7. KQ7 has script issues (parts of scripts in the game do not load correctly) so it isn't playable. LSL7, for the short time I played it - is.
To try to toubleshoot issues relating those games, go over the scummvm game file list (lists files necessary for each game) once more, and maybe - try a different source.
Broken Sword 1 doesn't work correctly (as is the case for other games as well), which is very well documented in this thread already. There is a general issue with the switch port of scummvm as of today - that causes (probably race condition related) crashes, when a game tries to load several resource files from the sdcard at once. (Several as in 3+, probably).
cpasjuste tried to track down the issue several times already, but since it seems to be partly related to libnx, its not an easy thing to fix.