With most double set, double lever triggers (such as yours), there isn't any easy way to take the slack out of them.
When the spring loaded trigger is set, the front firing trigger is engaged with a small catch (or trigger sear) on the spring loaded trigger. That's why only a little force and almost no movement of the firing trigger will release the spring loaded trigger.
If the spring loaded trigger is not "set", the firing trigger has to move past this position and continue moving until the blade on it contacts the locks sear release arm.
When custom building a gun, it usually is possible to file this blade so that it just barely clears the locks sear release arm, thereby reducing the overtravel, but if more material is removed from the blade (such as in a commercially made gun where safety and loose tolerances are the key words) a sloppy feeling trigger will be the result.
The only two ways to get the blade up close to the sear arm to reduce this overtravel, is to increase the depth of the trigger mortice, or to weld material back on the blade and custom fit it for that rifles locks sear arm position.
If you do decide to increase the trigger mortice depth, be prepared to do a lot of filing and adjusting to get the position right. If you don't do this correctly, your gun will be very dangerous and could fire at any time.
I hope that makes sense to you. :: :shocking: