Hi Mark,
On the ser1,2,&3 XKE, the "hump" between the seats is bigger (taller, wider, longer) on the automatic cars. As the automatic trans is about 9" longer than the manual trans, the rear mount has to be fabricated and the drive shaft shortened. The radio box and center console covering all that are also different than the manual XKE.
On the XK140 and 150, it's the same story, but the hump is removable. Switching a 140/150 to auto is straight forward, but if you go with original parts, the auto shift lever is on the bottom center of the dash - an engeneering nightmare. I'd advise getting a floor mounted one from an XJ or auto XKE.
I know of an automatic XK150 DHC that had a total rest. a few years ago. I think the guy wants $45K, but it's drop dead beautiful. It's dark blue with grey int. It would have been sold a few times if it were a stick, automatic is not that popular. It's a lot of money and it's way out here in S.E. PA. but it would cost twice that to build.
Send me a message if you have an interest or if you hit Lotto.
Phil.