READ THIS IN FULL BEFORE STARTING ANYTHING SUGGESTED
I solved this by re-building GitHub - GloriousEggroll/proton-ge-custom: Compatibility tool for Steam Play based on Wine and additional components from AUR and patching in the commit mentioned earlier for wine. Latest version of the launcher now works fine.
I’m using Manjaro with Lutris for EVE specifically, so YMMV. This should also work just fine for Arch Linux. Other users of inferior distros will have to adapt. 
I basically just added the adapted patch from my own gist, as proton-ge-custom has wine as a git submodule and the paths are different.
# create build dir
mkdir -p ~/build && cd ~/build
# get pkgbuild for proton-ge-custom
yay -G proton-ge-custom && cd proton-ge-custom
# download patched PKGBUILD file
curl https://gist.githubusercontent.com/TyrHeimdalEVE/a9ce15b8a3fd6cf56348e42dd4cea000/raw/8b2975fb5458a869e9943d8c0461fecee3aae872/PKGBUILD > PKGBUILD
# build and install
makepkg -sri
I also had to declare in Lutris to use the native DLL for msvcp140_1 before builtin.
(see: https://i.imgur.com/pnDaowP.png for how this is done).
Note, the above is equivalent to running:
WINEDLLOVERRIDES="msvcp140_1=n,b" path/to/proton/bin/wine eve.exe
Or if you use Steam for EVE:
WINEPREFIX=~/.steam/steam/steamapps/compatdata/8500/pfx winecfg
(see: https://i.imgur.com/1CGh5Sd.png how to set it, using winecfg)
The issue is, to my understanding - caused not only by the missing functionality in wine itself, but the builtin DLLs provided in the wine prefix doesn’t have it either (but it is bundled by CCP). This is probably why some get to the “Checking GUI Version…” screen, while others just hard crash.
If this saved your bacon, feel free to send me some iskies for PvP. 