The game on GOG works flawlessly for me, but once I install classic rebirth (following Carci's youtube guide), the game either crashes after the intro, or if I use another colour scheme, opens a completely broken menu.

Is there any known fix?

Using dgvoodoo v2.64 worked for me:

https://dege.freeweb.hu/dgVoodoo2/bin/dgVoodoo2_64.zip

Following this guide:
https://classicrebirth.com/index.php/re1cr-troubleshooting

Set VRAM to 4GB to prevent crashing after first door:
https://www.moddb.com/mods/resident-evil-hd-mod/downloads/resident-evil-hd-mod

Following the guide, I get the error message "Failed to initialize the DirectX".

i have an issue where the game doesnt want to start as the usa version of the game, and also doesnt start when i install rebirth to the japanese version of the game. the vanilla japanese version runs without issue and re2 runs without issue. idk what the issue is here and i've been looking.

You have probably fixed this already but if you are still having issues try updating your direct x with the redist that covers dx 9.0c Probably need the sourcenext patch and exe to get it to work with rebirth. although the other problems are strange.

yeah, i've been trying to look into my issue and i've been back with zero results. bizzare

Honestly just shots in the dark here but make sure all drivers are up to date and like i said previously get the dx back dated drivers i am sure its called 2016 SDK or something like that and i am sure google will point you in the correct direction otherswise honestly its a stump from me, however check you tube videos of how to install REbirth on re1 and then look on the forum here to install mods on re 2 and see if that gives you anything better with the game launching, be sure to install the games in Japanese on GoG though and with luck that helps you as the mods come with auto aim and such with them and the originals dont. HD packs are optional although i would reccomend them as well.