The following comes with the caveat that I am not a big lifter in bench. However, people I've offered the same tips to in person have added 10-15kg to their top lift, so there must be something to it.
Try putting plates under your feet, that'll make it easier to ground them.
Widen your grip a bit. Ideally, your elbows are always right under the bar, to ensure you have good pressing strength. If your elbows are forward or behind the bar, you're not able to deliver the full force from your chest, some of it is going to hold the weight in that funny position.
If your grip is very narrow or very wide, then you can't keep your elbows under the bar. So find something in between. You'll have a more solid feel to your press and know pretty quickly when you've got it right.
Aside from that is just the things you yourself have seen. Keep your head on the bench. To achieve that, when you grab the bar at first, bring your shoulderblades together. Then press straight up, and only then bring the bar forwards over you.
That way, you have the best chance of keeping your shoulderblades together, and have a firmer base to press from. And your head is more likely to stay down, too.
Though once you go heavy, you won't be able to keep your shoulderblades together without someone giving you a lift off.
The grip issue is probably the main one, and fixing that should add a chunk to your lift. The other stuff just a little bit.