One way to a bigger and more stable bench is a strong upper back, since ive personally started kroc rows ive had no stability issues.
Some ppl promote flaring as a means to get the most out of your lockout strength, just keep making sure the bar is being pulled apart. I almost always flare on heavy ME work. Just aim to press in a straight line and maybe warm up with a band around your wrists. If you get a chance post some vids of your bench.