I have yet to see a Full choke tube that is rated for use with steel shot (or tungsten) that didn't say it right on the tube, but I haven't seen them all. I know Remington was the first, and for a long time the only, manufacturer that made a steel rated flush Full tube, because they used maraging steel. Others have jumped on the bandwagon. What does your Flush Full choke tube say on it?
Larger shot does indeed usually pattern tighter with more open chokes than smaller shot. Improved Modified works well for #2 and bigger in my experience, assuming of course you are looking for the tightest patterns you can get. Brileys has a good discussion of chokes and patterns on their web site.