Yep, no half ****. Not even a rebound feature like some back-action locks have.
The rear trigger bar in #7761 is what's keeping the lock from cocking unset. I can see from the front trigger position relative to the plate that the front trigger bar isn't what's holding up the works, if it even has a front bar that would enable it to fire unset (double-acting type).
The general advice is to file down the rear bar but this is usually the wrong thing to do because it weakens the bar and removes mass it needs to work properly, unless it is just grossly too tall. Sometimes a combination of filing down the top of the rear trigger bar and limiting the trigger mainspring travel is necessary, but usually if it works by pre-setting the trigger then the mainspring overtravel is all that needs adjusting.
Pull the **** to full **** position with the triggers unset and hold it there. Then pull the rear trigger very slowly until the lock's sear bar engages full ****. That amount of rear trigger movement should be FREE. No spring pressure at all on the rear trigger. With the rear trigger unset and the lock at full **** (which it won't currently do), there should be a teensy amount of free play in the rear trigger. When set up properly, the trigger mainspring only engages the rear trigger at the very back end of the rear trigger's travel, allowing the sear bar free movement into the full **** notch. Then the rear trigger can be pulled farther back against the mainspring to set it, and when the front trigger is pulled, the loaded rear trigger releases and slaps the sear bar, activating the sear bar through inertia only. The rear trigger mainspring should never force the rear trigger bar to touch the sear bar directly at any time, but "flings" the rear trigger at the sear bar and stops against the trigger plate just before the trigger bar hits the sear bar and the inertia of the trigger then carries through and fires the lock.
It's like a billiard shot. The trigger mainspring is your arm, the cue stick is the rear trigger, and the sear bar is the cue ball. The stick and cue ball only touch for an instant to transfer the energy and the is no follow-through contact.
Remove the trigger assembly and note where/how the main spring contacts the rear trigger and what the mainspring stops on. Either raise the stop, file the jose of the mainspring, or file the part of the rear trigger that the mainspring nose engages so that the main spring doesn't force the rear trigger to keep the sear bar disengaged from the full **** notch. You should be able to install the lock in the rifle fully cocked and with the trigger NOT set. I dislike the arrangement you have now because it makes it very difficult to thumb the hammer down gently. Hope this helps some.