Hello @ranulf
I'm sorry for my delayed response.
For the flashing algorithm, you are right: for the generated elf file, the default flashing algorithm needs to be used, while the RappID bootloader requires a different one, as specified by you above.
I am not quite an expert in S32DS but I might have a solution for the case with the default flashing algorithm and not booting after reset. My idea is to change the linker file to not include the boot information required by the RappID bootloader.
To do so, please add the attached linker file in the window opened by typing the following command in MATLAB's command window winopen(fullfile(mbd_find_mpc_root, 'mbdtbx_mpc577x\src\linker\gcc'))
Then go to the model config block, uncheck the "Download code after build" option under Target Connection, then go to the Build Toolchain Tab.
uncheck the "Default Target Memory ..." and you should be able to see the new linker file under that option.

If the linker file option does not appear, try reopening the config block. If still, you are not able to see the newly added file, just replace the old one, but backup it before because without that one you will not be able to reuse the rapid bootloader again.
Let me know if this solved the reboot issue.
Hope this helps,
Marius