I haven't personally messed with the Savage triggers, the few I have been around had decent triggers, but were just the basic accutrigger, not the target one. But from the sounds of it, to me I would think the sear engagement of some form is the issue, or possibly the inherent design not maintaining enough pressure on the sear while the bolt is closing. I am assuming that there isn't much of an adjustment for the sear, or it would have been mentioned. What I have found from messing with triggers on many different guns, is if you mess up the sear, there isn't really a fix for it, as you can't really add material where it has been taken away, or possibly in this case, was never there to begin with.
But, if there is enough sear engagement, possibly look at the sear angle? If the engagement surfaces don't mate up well, this could lend itself to your issue. I may be way off, but this is what I would start looking at. I also like to tinker and learn, and when I mess with things like this I often go into the project fully expecting that I may have to fully replace it in the long run anyway. But hey, if your going to buy a replacement, you might as well learn something along the way. At least for me, that is how I always justify my tinkering and breaking of stuff, ha ha.