The problem here seems to be that you are looking for a particular exercise that will singlehandedly increase your bench, and it’s not that simple. OHP may or may not help, some people swear by it while other do none at all and bench big weights. It will help if your shoulders are holding you back, but otherwise the benefits will be marginal at best. And you are doing 5/3/1, aren’t you already doing ohp?
Another issue is that you don’t want to gain weight. Bench press strength is affected a lot by muscle mass. Without gaining weight, the things that will help most are perfecting your technique (which will require more than two work sets per week) and using special exercises to target weak points in the lift.