I have a slightly different take since the original poster is a fighter. I've always thought that lifting weights in preparation for fighting (including wrestling, BJJ, etc.) should be done to increase endurance as much as strength. When I was training harder, I liked to run right before lifting weights (running hard, sometimes even with a few sprints at the end if there was a track available). It definitely made me tired and decreased the weight I could use, but I felt it mimicked the type of strength I was looking for (i.e. being able to throw a guy in the third period or put together a hard combination in the 4th round).
I don't have any science to back this up as the right approach, but it might be something to try for a few weeks. It's definitely not a way to increase your bench press, but you might find your functional fighting strength improving.