Veneto, ItalyThe DIGIretroBOY (aka Revo K101+) looks like an hardware clone and it seems that it packs also the original GBA BIOS.
Might be worth a shot running some test ROMs off the microSD adapter to evaluate whether it runs at the original framerate, especially considering that even the Analogue Pocket runs faster than a GBA as it stands (so again, only IGT can be submitted).
If you want to go down the real hardware route, GameCube + GBPlayer would be the cheapest way to play comfortably (NTSC-J consoles are readily available, at least here in Europe and can be modded to be NTSC-U by moving a resistor on the motherboard).
Cost cutting measures might be installing PicoBoot on the GC (soldering required) and using an SD2SP2 (microSD -> serial port 2, the latter is present only on the early GC models) so you won't need the GBPlayer boot disc since you can just fire up either GBI or a dump of the disc off the SD card.
To have digital output (namely, HDMI) out of the GC you'd have to fetch a GCVideo compatible dongle (uses the digital port present only on the earlier GameCube revision), which goes for anywhere from 35 to 50€ from the usual suspects such as AE, definitely more if you're buying locally. Remember that no NTSC versions of the GC output RGB.
Another solution might be modding a GBA (I don't think there's a kit out for the SP, yet) with one of the IPS screen + TV out kits, but you'd be bound to have a pile of AA batteries to run the console, plus not all TV out kits output HDMI, rather they output composite which got its obvious downsides.
Needless to say, the cheapest solution of them all is to run on the only approved emulator, as in Bizhawk using the mGBA core with a valid BIOS dump loaded. In that case you need only your own PC and a bare minimum OBS setup to record the emulator output and eventually the timer. Seeing your previous submissions that it seems you're on Linux, you can run Bizhawk on it too by installing mono and libgdiplus as requirements.
If I recall correctly, the Retron SQ just dumps the contents of the cartridge and runs it through an emulator.
Two issues arise: the emulator Hyperkin products run is pretty much unauditable for accuracy, the other being that for sure Hyperkin doesn't bundle the GBA BIOS into the console for copyright reasons, which means that it's automatically banned for RTA timings because the emulator is going to use reverse engineered (and faster) default routines rather than the ones coming from the BIOS, potentially giving an unfair advantage versus people using Bizhawk w/a BIOS dump or actual hardware.
Secret message counts as just triggering it or doing the entire shinespark chain? Because on the English version you can just freeze the Powamp by doing missiles momentum shenanigans without having diffusion and still get the message:
If I recall correctly, the RetroN 5 runs a fairly old (and license violating, since no sources are available) version of SNES9x Next that might fall into the list of banned emulators as per game rules.
Since the sources for the emulators built in into the console are not available to the general public, the only ways to evaluate its accuracy can be either disassembling the firmware of the console to check the emu version or have mods do an empirical analysis of a recording.
My two cents: if you're going to tackle running the game, you're definitely going to get better accuracy by emulating the game on your PC instead of an underpowered "single purpose emulation box". Whenever you feel confident with going further down the RTA rabbit hole, you can bite the bullet and pick up a console + a flashcart for it or an actual SM cartridge.
