If there is any way consider a cooktop and a telescope vent. The telescope functions better than the flat vent on the JA.

My JA downdraft cooktop a was not effective in removing fumes and vapors. At full power it pulled in only about half of what a vent system should. The shorter the pan wall the better it works. Stockpots are out of the question. Look for any possible alternative in my opinion.

When we purchased our house 5 years ago we replaced the Jenn Air electric cooktop with downdraft vent with the gas version [I think after Googling your model number you are considering the gas cooktop]. One major warning a friend gave me was the vent "pulled" the gas flame. After talking with another friend who had the same model, her comment was, "With the gas it will be so much better than what you've had, you'll love it". OK, so she was partially right; I eventually felt like I cooked on a habachi griddle, I would move the food around to cook on the hotter or cooler portion of the pan.

I did not realize how noisy & ineffective the vent was (low speed [2 speeds]) until we just remodeled & replaced with a Kitchen Aid 36" gas cooktop & Zephyr Island hood (42") -- amazing!!!! Now, I understand you may not be able to go with an island hood -- we removed the sheetrock & vented through the joists on 2nd floor out to our deck. If you can't do that research the telescoping downdraft vent. It may still pull the flame, but it will be more effective than the 2-speed Jenn Air.

Also, this Kitchen Aid cooktop was some type closeout or special purchase at BrandsMart (Atlanta & other SE locations) for $300 last fall!!!! It is working so beautifully we are amazed & giddy.

You also mentioned the Jenn Air finish. That was also odd for us. We paid extra for "stainless steel" & all that was stainless was a 1" border on black enamel/porcelein trays. The stainless was to be cleaned "with the grain" which was wiping 1 inch all the way around -- I felt very frustrated trying to clean up.

Additionally, we purchased (or perhaps received at a reduced price) the griddle. Since this was 4 burner, it was not a module we would leave in all the time, but even when we used it (TWICE!!!) it forced the vent & the gas temperature to be on high & was unbearable to listen to & cook with/burn with. Perhaps newer models have improved, but definitely don't pay extra for the griddle.

My friend was correct, the gas was much better to cook with than electric, but I'm glad I no longer have this Jenn Air cook top.

As suggested early on, I would recommend a rear downdraft vent system like Thermador's:
http://www.thermador.com/Product.aspx?product_id=296&cat_id=747&collection_type=1&product_width=30
I just took out our old Jenn-Air and we also had one at our last place (neither of them of our choosing). Both sucked, and I don't mean in a good way! Ventillation is noisy, inefficient and they do suck the heat/flames sideways, right out from under the pans. How inefficient! Such a loss of heat!
Get a good downdraft unit and may I suggest that you look into an induction cooktop? Especially for those like you, who can't vent from above, a non-gas cooktop makes a lot more sense. Less heat going out into the room and no gas fumes!
We are extremely happy with our Wolf induction cooktop and we considered Thermador. I am a serious cook, and have been for 50+ years. I used to have a Thermador six-burner gas stove (that I loved), but now I don't miss the gas at all. It performs very similarly; very responsive.