Currently, the crafting recipe for the cart assembler is incorrect on the 'Blocks' page. I only figured out the correct recipe after using the 'Uncrafting Table' mod by jglrxavpok, csb987, and Nevik_9191. For anyone that is searching for the correct recipe it is as follows:

If this isn't the case for anyone else, then I could be having some other mod interference, although I'm not sure how that could work.

I have the following 1.12.2 compatible mods installed (listed by file name), but everything else has been working perfectly.
-Backpacks-Mod-by-Brad16840-1.12.2
-Chameleon-1.12-4.1.3
-ColorUtility-universal-1.0.4
-RebornCore-1.12.2-3.6.11.220-universal
-StevesCarts-1.12.2-2.4.18.92
-StorageDrawers-1.12.2-5.3.5
-Uncrafting-Table-Mod-1.12.1
-WearableBackpacks-1.12.2-3.1.2