Yes, Binkie, you gave away
rung while the puzzle was still live. But then, I did say just the other day that I've given up trying to enforce the rules in the forum, so forget I mentioned it, I beg of you.
Anyhow, what of
runged? Well, the Shorter Oxford says it's a word, meaning of course "having rungs". And as you and Threeb point out, it is in use. A couple of examples from literary sources:
What, you want, do you, to come unawares,
Sweeping the church up for first morning-prayers,
And find a poor devil has ended his cares
At the foot of your rotten-runged rat-riddled stairs?
Robert Browning, "Master Hugues Of Saxe-Gotha"
...the sofa—a light, wooden, batten one, with runged arms at the ends...
Henry Lawson, "No Place for a Woman"
So
runged will be added to our list.