My review for Secrets of Home Theater and High Fidelity of a complete LSiM system should be up soon, but to be brief I don't think the 703s are going to give you a "warm" sound. They are a very neutral sounding speaker. You can influence them with richer/warmer sounding components, but they don't have a definitive signature of their own. Frankly, I think they are an incredible value for the money. I've been using the 703s in place of my Paradigm Studio 20 V3s in a 2-channel setup and haven't been missing the Studios much (though I still love the old girls). The 703s have a slightly flatter frequency response. The Paradigms have a bit of a mid-bass bump that gives them subjectively more bass impact. Hence it sounds like the Paradigms go deeper in my room, but they really don't. The Paradigms are a bit more sensitive, so that could be important depending upon your amplification. Mid-range/treble detail is superior on the 703s.
What are you using for source components/amplification?
I agree with 60strat's comments on JBLs in general. Defintely bright and a bit more forward from my experience.
Have you considered the Dynaudio X16? Excellent speaker in a similar price class to the Polk. What about something from Sonus faber or Vienna Acoustics? They will give you a slightly richer presentation without sacrificing detail.