the issue with that swap is the 16 tooth tone wheel , and the fact that your Jeep is a JTEC PCM , we've changed 4.7s with the 32 tooth tone ring to 5.7s a few times, and have even tuned the 4.7(NGC3&4) pcms to run the 5.7.
If you swap the ECU over to a NGC3(NGC4) you can run the 5.7 on the 4.7 PCM, but as for dash cluster I can not answer that, Might look into swapping a dash cage & cluster from an 05 Jeep in to your 02, I don't know if that's a possibility , I don't know the jeeps that well..
My brother did an 02 Ram a few years back were he took the dash cage, instrument cluster and PCM out of a 2014 , put it in the 02, I know it's apples to Jeep comparison but it might be something to look at( the whole swap from 05 Jeep to 02 jeep)
As for the LS conversion, it's harder than people think, almost everything is a Painless wiring swap...
just a thought might want to contact DIY hemi swap , they might be able to help you