tl;dr - If you want to sign in with your regular account, right click on Guild Wars 2 in your steam library and select Properties. Then paste -provider Portal into the "Launch Options" box.

Guild Wars 2 on Steam only downloads 3 files - Gw2-64.exe, Gw2.dat, and installscript.vdf. The executable and dat are the exact same as you've been using for years, there's no difference between the files included in a Steam install and the files included in a regular install.

Because of this, if you want to install the game on Steam without redownloading the entire thing, all you need to do is copy Gw2.dat to steamapps\common\Guild Wars 2\Gw2.dat. If you do this then install the game, it will "download" basically instantly.

When the game is run through Steam, internally it runs Gw2-64.exe -provider Steam. It's not doing anything fancier than that, it's simply a launch argument This is visible here, on SteamDB.[steamdb.info]

Knowing this, we can very easily override the provider from steam to the regular account system by overriding the provider argument. This is as simple as adding -provider Portal to the launch arguments, which superceeds the built in -provider Steam argument.

To do this, right click on Guild Wars 2 in your steam library, and select properties. Then paste -provider Portal into the "Launch Options" box.

Knowing this, we can very easily override the provider from steam to the regular account system by overriding the provider argument. This is as simple as adding -provider Portal to the launch arguments, which superceeds the built in -provider Steam argument.

To do this, right click on Guild Wars 2 in your steam library, and select properties. Then paste -provider Portal into the "Launch Options" box.

CANNOT buy the expansions or Living World content through steam using this method. The licenses for those will be applied to your Steam account, not your existing Guild Wars 2 account.

Thanks to Jademalo.