Be *very* careful not to be crushed.

In particular:

Be *very* careful around elevators.
In the Mine Tunnels, stand away from the mine cart when moving that wood. I have been crushed by it. (Fortunately, I never play Iron Man, but I could see this being incredibly frustrating for an Iron Man run to be ended because of this.)
If you go out-of-bounds (like a trick I mentioned in the Upper Monastery), be careful, as going too far will get you crushed. (If you want to play around with glitches, I suggest *not* using an Iron Man file for that purpose.)
Beware of the Umpani obstacle course. That part in the game can kill you (either by crushing or lava), and is a part I don't consider to belong in an RPG. I recommend either doing this early (so you lose less time to the defeat) or not joining the Umpani at all. (I might go as far as to recommend backing up your save before that part, simply because I don't think it's fair to have an Iron Man run of an RPG to be ruined by an action game sequence.)

Note that this advice does not depend on your party at all.

Honestly I'm not a big fan of game-imposed Iron Man challenges. I like player-imposed ones a lot better. That way, if something goes wrong, you have the option to start over, but you also have the option to simply continue your playthrough in non-Iron Man mode.

On a related note, my very first Iron Man playthrough ended when my party was crushed by a BOX LID in the Upper Monastery. A box lid.

The Gregor fight can | should be avoided for another level... take the bridge lift up to do some shopping then you can jump back down... at level four your party should be able to handle the fish and get the rez dust.

Gregor or not: you'll enter fights you don't win. Maybe you had a couple of easy fights and believe the next just as easy until something unexpected happens. Maybe you are surprised by some really strong opponent. Maybe some specific fight is specificly hard for your party, compared to your last playthrough.

Whatever you do: you need a backup plan. You need to be able to run. Dead ends can be quite the literal end they promise to be by not allowing a retreat. Also an elevator or other things can spell the end.
As I see it Iron Man with a full party isn't too much about hard fights but more about accuracy. Your party can slaughter it's way through the lands and yet fall into some trap or another due to sheer carelessness - especially if they are strong enough to slaughter any opposition for a while, which lures into a false sense of security.

In fact the earliest instant death I faced, luckily not in an Iron Man game, was the door to the Monastery, which slew my party. That's really rare, just like the box lid I imagine. Just NEVER rush things around the moving parts I guess.