I've no doubt that the pic above does show "a Batmobile" with an FE.
However, there were at least 3 other complete running Batmobiles built after the 1st one, all by Barris and IIRC one by someone else much later. Then, as in my previous post, many copies were later pulled from the 2nd or 3rd car by a fiberglass body maker, rumored to be the old funny car body maker Fiberglass Trends Co. Many engineless copies on rolling frames (see Volo Auto Museum site) were made and shown at car shows. In fact, I remember seeing a Batmobile on the same weekend at two different car shows!
I did see pics of the 1st car long ago indicating a MEL was used in the Futura concept car while the Batcar was under construction. But it could have been a dummy engine (hey that's what show cars sometimes get) that later could have been switched to the more current late '64-early '65 FE design. Not a biggie in my book as it was rare to ever see the hood up. If the switch was made, it was likely due to more hp and easier parts availabilty. JMO.
http://www.1966batmobile.com/
