Besides the AD issue between EIGRP and BGP, I haven't labbed this, but I could suppose you also have an issue because you are running the iBGP sessions between loopbacks, which in turn are known via the IGP which is EIGRP and is not sync with LDP or any other label distribution protocol. You could try to run the iBGP sessions between the connected interfaces. (don't forget the "mpls bgp forwarding" command under the interfaces !!!!, or if you are using IOS XR the /32 static route to the connected interface on the other side !) In turn, you won't be requiring an IGP anymore.
If you could try this out, and let us know what was the outcome it would be great !