Okay, I took a few minutes to watch this video:
to better familiarize myself with the MG34 trigger mechanism. And in doing so, I found that the original trigger doesn't pivot (as I had assumed), it looks like it slides within the housing. If you want to use a pivoting trigger, this complicates matters a bit.
For a pivoting trigger, if it were me, I'd probably just saw off the entire rear of the trigger extension (along the yellow line on the image below), drill a hole through the trigger and trigger guard assembly at about the spot of the green dot, slightly enlarge the hole where it passes through the trigger itself (so it will swing freely on the pin), and secure the whole thing with a solid fitted pin or a roll pin. As the trigger looks a little thinner than I originally thought, I'd probably give up on slotting it, and just use the vertical rear face of the cut as the spot for the Marlin trigger to slide against (may have to fill any existing slot/gaps in the trigger with metal or high-abrasion-resistance polymer, so the tip of the Marlin trigger will slide smoothly along the face of the cut). Due to the location of the MG34 trigger and the tip of the marlin trigger, the MG34 vertical trigger cut may actually intrude into the trigger guard area, which means it may be visible in the final product. Finally, I'd add a trigger return spring near the bottom of the MG34 trigger (either a torsional spring with one leg bearing on the trigger and the other leg bearing on a pin of the trigger guard, OR, a spring and plunger contained in a small tube set back into the grip frame area, under the grips (whichever you think might be easier to fabricate/install).
For a sliding trigger, I would NOT cut the original trigger, I'd just remove the upward projection near the front. I'd probably shorten the Marlin's trigger so it stopped just above the MG34 trigger bar, then I'd fashion an upward extension on the MG trigger to "trip" the Marlin trigger when the MG trigger slid to the rear. You'd have to figure a way to contain the trigger so it only slid front-to-back a certain distance and then stopped (or build that distance into the extended "trip" lever), to prevent stressing the Marlin trigger, but you might be able to use the existing trigger return spring and with this type of modification, everything externally visible would probably look and move in a more authentic manner.