Yes, I seem to have got it working.
In my MQX project, I edited the startup_MK22F51212.s file in the mqx_frdm22f project found in the KSDK Files directory. In this file I commented DefaultISR 240-254 and also removed the DCD 0xFFFFFFFF value reserved for user TRIM value (is that okay?). In placed of that, I added the BCA area (0x3C0-0x3FF) like it was in the demo project.
Additionally, I changed the linker file (MK22FN512xxx12_flash.icf) to define the following symbols:
define symbol __ram_vector_table_size__ = 0x00000400;
define symbol __ram_vector_table_offset__ = 0x000003FF;
define symbol INTERRUPTS_START = 0x0000A000;
define symbol INTERRUPTS_END = 0x0000A3FF;
define symbol FLASH_CONFIG_START = 0x0000A400;
define symbol FLASH_CONFIG_END = 0x0000A40F;
define symbol TEXT_START = 0x0000A410;
define symbol TEXT_END = 0x0007FFFF;
define symbol RAM_INTERRUPTS_START = 0x1FFF0000;
define symbol RAM_INTERRUPTS_END = 0x1FFF0000 + __ram_vector_table_offset__;
define symbol DATA_START = RAM_INTERRUPTS_START + __ram_vector_table_size__;
define symbol DATA_END = 0x1FFFFFFF;
define symbol DATA_2_START = 0x20000000;
define symbol DATA_2_END = 0x2000FFEF;