Credit to Michael Chisholm, Adam Hodson and Maxim for the patching software and @piratesephiroth for sharing the DLDI.

Method 1 - Patch each homebrew manually. While arduous to do for every homebrew, it is the safest option and fairly straightforward.
 -Open "dlditool32.exe" in the "dlditool-win32-gui" folder.
 -Select the folder where your DLDI drivers are, then select which one you want to use from the dropdown menu. For the blue card, that will be "ex4tf".
 -Browse your PC for the .nds files you want to patch. You can patch several at a time.
 -Click the "Patch" button and let the program work its magic. It shouldn't take too long, and the log will show if the file has been successfully patched or not.
 -Open the homebrew on your NDS/3DS and see if it works.

Method 2 - Flashcard auto-patching. The simplest and quickest method, though I'm not sure of how safe this will be. Unofficial software/hardware mods have caused bricks of 3DS consoles in the past. 
 -Copy the GW blue card firmware from version 3.0.4 public beta to your flashcard.
 -Copy "game.dldi" into the "__rpg" folder and replace the old one.
 -That's it. The flashcard should automatically read the DLDI file when you open homebrew.

Source: Analysis on the Gateway 3DS blue cart (updateable??) @ https://gbatemp.net/threads/analysis-on-the-gateway-3ds-blue-cart-updateable.357103/page-4#post-5115827