When you pull your wood from your steambox, IMMEDIATELY get it on the mould, round, in under 10 seconds. The wood is cooling off at the end of your rim strip. You can't steam it, dry it, bend it, cook it, or beat it into shape if it's not round under 10 seconds. And don't oversteam your wood, you'll crack it. The perforated steel won't help.It's a two person job.
How long at what temperature do you steam it? .. and how long does it take you to get it on your round jig? You're wasting time waiting for it to become round if you don't get the first three steps correct. The steel with holes won't help.
I've had good luck by: 1) like Terry said - getting the steamed wood bent around my jig as soon as it comes out of the steam box. I have trouble doing this by myself and have to get someone to help me. 2) I put the whole thing - clamps and all - in the oven at 200 degrees and set the timer to turn the oven off after 4 hours. I have to wait until my wife goes to bed before I can do this without getting yelled at. The next morning I take the rim off of the jig and glue it up. I've never had trouble with warping, but have had trouble with the rim being out of round if it doesn't get clamped onto the jig as soon as it comes out of the steam box.
When you're putting the steamed wood on the mould / jig, and you feel any stiffening of the wood, start over. It should go on like a big wet noodle. It's the ONLY way to make a ROUND rim. They cannot be fixed after this step. Even if you did get a mishapen rim round, it's likely to change. They have to be on the jig in under 10 seconds, that's oak and ash. Maple is persnickety. It wants to bulge and bend in strange places. Maple is boring visually. For the lighter color, just use ash instead.