One thing nobody mentioned yet — before you even touch gains, verify your inertia ratio. Run the Yaskawa auto-measurement (Fn00B) with the die out and slide at mid-stroke. If the measured inertia ratio (Un00D) is above 15:1, you're going to fight tuning forever. Our 300T was showing 22:1 because the coupling between motor and ball screw had worn — 0.08mm backlash that the encoder couldn't see.
Also be careful with Yaskawa's auto-tuning (Fn002). It works great on simple linear axes but on a press it tends to set the speed loop way too aggressive because it tests with no load. I've seen it set Pn110 at 500+ which is asking for trouble once you hit material. My approach: run auto-tune, then immediately cut Pn110 by 40% and Pn102 by 30%. That's your real starting point.
The other gotcha with SGM7J specifically — check Pn00B (motor code). If you replaced a motor and the drive still has the old motor code, the current loop parameters will be wrong and no amount of speed/position tuning will fix the vibration. Ask me how I know... cost us two days on a weekend changeover.