As long as you didn't rebind any keys that weren't bound by default, and didn't turn on "always mouselook", you were pretty close. For GZDoom, there is also the excellent Vanilla Essence mod that allows you to very quickly enable the whole "vanilla style" with the push of a button. You still get your neat sounds that way, and you don't have to step away from your usual sourceport.
If you're absolutely worried about purism, try playing the game in Chocolate Doom. It's the closest you can get to the 1994 DOS engine without running DOSBOX. The Sprite Fixing Project and Perkristan's sound effects still work with that. Plus there's some really neat "vanilla mods", like Rekkr and D4V, that use that port as a baseline.
Alternatively, Crispy Doom's current stable release has proper autoload (useful for the linked enhancement mods), it has a bunch of nice engine enhancements, which are all optional. By default it runs "Stock doom" + bug fixes + a higher resolution. You can set for yourself how "enhanced" you want your Doom to be, with the port being very clear about what is stock and what is not (eg the more green text you have in your "Crispness" screen, the further away from Vanilla you are). It's my personal favorite for running vanilla compatible stuff, esp. since I can just turn off all the enhancements, including the increased resolution, and just have it load up a pwad whilst it autoloads the sprite fixes and sound packs for me.
PrBoom+ supports 'as vanilla' but that already requires a bit more fiddling with the correct complevels (eg using the -complevel 2 and -complevel 3 command lines, as by default PrBoom+ runs Boom). In my personal experience, I found it to be a bit of a weird bastard between GZDoom and Crispy. I know for a lot of others it's the sweet spot but centrism is for cowards if you want to go vanilla, just... go vanilla. You have those options. Embrace the fact that you can't run it at a fancy widescreen resolution with the increased FOV. Embrace that 1994 doom was built upon compromises upon compromises which all subsequent source ports have tried to remedy. Experience that despite being incredibly technologically limited it still is a fun game. Or reject that entirely, in which case GZDoom is for you!