Go for the recirculating for sure. Make the hood capture area 36" by 27" if possible with a 600 cfm blower mounting that 30"-32" above the stove or as low a practical. Ditch the downdraft idea HUGE MISTAKE......

A recirc will pump all that waste btu heated air out throughout your space. An alternative is induction. Better response and lots of power without those thousands of btus. You have the in place venting for the Jenn Air. This downdraft coming in January could use that. This and other downdrafts can usually mate to any cooktop if you allow space as per the install instructions.

http://www.prnewswire.com/news-releases/the-new-cattura-downdraft-from-best-melds-best-in-class-performance-with-sleek-design-300021762.html

The only "approved" approved induction setup that would let you vent out is the Dacor range with the matching popup downdraft. You might get another combination to work, but it could be difficult to fit the popup especially if this isn't an island application (which it sounds like it isn't). Your existing range is probably dual fuel (I don't think JA ever made all-gas downdraft ranges) so you would have a 240 line for it. It's definitely an option to consider if you haven't already.

However, it's a personal preference. If you prefer to cook on open gas burners, I wouldn't give that up just to vent out, if all you're going to get is mediocre (downdraft) ventilation anyway.

Here's what may well happen with the recirc

http://ths.gardenweb.com/discussions/3336120/how-do-i-change-our-venting-situation?n=7