As suggested by Kubilay in Comment #2 of pr 211217 [1] rather than using an option to decide which toolkit to link against, provide both via slaveports.
I opted to not rename the existing port to sqlitebrowser-qt4 [to reduce the changes] -- even though that might be cleaner.
[1] pr211217
I'm seeing build failures at cleandir stage. I guess LINKER_TYPE isn't being defined at that point. So ${LINKER_TYPE} would need to be wrapped in quotes, or for LINKER_TYPE to be defined at all stages.