Mupen64plus FZ should run Zelda and Doom64 a lot better than in the old +AE version, but it might depend on your device.
Have you adjusted the emulation profile settings in the FZ edition for improvements?
Because the default FZ settings are different from the +AE version.
Sometimes if you download more than one mupen based emulator there can be errors due to multiple mupen folders, and files stored in
one folder may be linked to a specific emulator.
I'm not sure if FZ savestates are compatible with the AE version, but maybe give this a try:
Back-up your savestates and settings from the mupen64plus-fz folder, then delete both Mupen64plus FZ & +AE apps and all their associated folders.
Reinstall your preferred version FZ / AE and import your savestates/settings into the folders.