Resting definitely helps. Also, try ice water and not just ice---more contact.
I happened to be sending IMs back and forth with a professional brewer friend of mine while reading this and asked him, since he's poured many a beer through a jockey box at beer festivals. His answer: if you have a coil, the kegs need to be iced. If you have a cold plate, you can serve from warm kegs without worry as cold plates are more efficient.
And like a home draft system, the jockey box needs to be balanced...ie. the right length and diameter of tubing, the right chilling apparatus, as Bobby alluded to.
Mine uses an aluminum
cold plate that adds enough restriction to balance it, and it's worked great for me.
Good luck with it.
Cheers!