No, you can't do that , the difference is not in the tail section the difference is in the centter section (with the red NP tag on it and the drain/fill plugs), not in the casting itself, but how it is studded.
The studs are installed in different locations to alter the clock orientation of the tail section, you need to move a some of them to be how they re installed in the Eagle's case....this may require a drill and a tap, but I think its only 1 or 2 studs that move.
The 90-deg adapter could be an easier fix, but I don't know where to get one, and I'm not sure if the speedo cable will be long enough to reach the new adapter location.
I agree if you go with an off-road specialist like BJ's, and you contact them, they should put together a "kit" for you even if it is not boxed that way from a manufacturer.
You mentioned that you want the 229 because it is full time, just though I'd mention the Grand Cherokee's 249 is a lot more recently made and a lot more common in the time it was made, uses the same case, and you will have a easier/cheaper time getting parts,
but the initial install will require rear driveshaft customization as the slip yoke goes into the T-case instead of being in the middle of the driveshaft like on the eagle and FSJ
NP249 will also eliminate the vacuum system (I consider this a plus, others I'm sure will not) as the lever will control all ranges instead of just the low range...it also has a N, but doesn't have a 2wd range.