Hi Karl,
first, you need to force BOOTCFG1 to '1'. This signal is available only on SIPI connector, pin 9.
To confirm you are really in serial boot mode, you can connect a debugger and check SIU_RSR register. BOOTCFG bit field should be 0b01.
I confirmed the baud rates listed in the reference manual are correct. There's 40MHz crystal, so the baud rate is fixed to 48000.
Notice that we have Rappid bootloader utility:
https://www.nxp.com/webapp/Download?colCode=RAPPID_BOOTLOADER_UTILITY&appType=license
In case of MPC5777C, there's only RBF version. It does not use this serial boot of BAM, it's flash resident bootloder. So, you need to program it via JTAG to flash and then you can use the utility to program an application either via UART or CAN.
Some additional custom RBF files can be found here:
https://community.nxp.com/t5/S32-Design-Studio-Knowledge-Base/RAppID-Bootloader-custom-rbf-files/ta-...
Notice that it's proprietary code, we do not share the source files.
Regards,
Lukas