Robotmike2
a couple of these programs look they are built to sync the joystick:
$ flatpak search joystick
Name Description Application ID Version Branch Remotes
jstest-gtk jstest-gtk - A graphical joystick tester …ab.jstest_gtk.jstest_gtk 8e84777 stable flathub
AntiMicroX Graphical program used to map gamepad buttons to keyboard, mouse, scripts and … …ub.antimicrox.antimicrox 3.3.3 stable flathub
godotGem Controller client to emulate an xbox360 controller for windows …SlammedMyKindle.godotGem 1.2.0 stable flathub
sdl-jstest Console based joystick test program for SDL …ab.sdl_jstest.sdl_jstest v0.2.1-11-g269f727 stable flathub
sdl-jstest Console based joystick test program for SDL …b.sdl_jstest.sdl2_jstest v0.2.1-10-gb6c9d96 stable flathub
Hatari Atari ST/STE/TT/Falcon emulator org.tuxfamily.hatari 2.4.1-1 stable flathub
SuperTux - M… The classic version of the platformer starring Tux the Penguin …rtux.SuperTux-Milestone1 0.1.4 stable flathub
Hikou no mizu Platform-based, anime-styled fighting game ….hikounomizu.HikouNoMizu 0.9.2 stable flathub
TORCS The Open Racing Car Simulator net.sourceforge.torcs 1.3.7 stable flathub
Frets on Fire Frets on Fire is a game of musical skill and fast fingers. The aim of the game… ….sourceforge.fretsonfire 1.3.110 stable flathub
SDL-Ball Brick-breaking game with pretty graphics net.sourceforge.SDL-Ball 1.04 stable flathub
Fuse Sinclair ZX Spectrum Emulator net.sf.fuse_emulator 1.6.0 stable flathub
Kobo Deluxe Third person scrolling 2D shooter net.olofson.KoboDeluxe 0.5.1 stable flathub
openflap A game about bouncing balls through gaps of never-ending pipes …lab.jazztickets.openflap 1.0.6 stable flathub
Bombermaaan Arcade Game …hub.bjaraujo.Bombermaaan 2.1.8.2208 stable flathub
this from the repo might be short of mark (Attract):
"Attract-Mode is a graphical frontend for command line emulators such as MAME, MESS, and Nestopia. It hides the underlying operating system and is intended to be controlled with a joystick, gamepad or spin dial, making it ideal for use in arcade cabinet setups."
This is just stuff to try. I have no personal knowledge of which program would get you where you want to be with the re-alignment. edit/format