Minecraft – How to migrate from one MC map to another retaining all collected items

You can use the Dolly from JABBA to move vanilla chests, chests from Iron Chests, BC Tanks and machines Thermal Expansion and IC2. Be careful as it can't move Factorization Barrels, or Better Storage Chests. It's a good tool for reorienting said blocks.

When you have a filled dolly in your inventory you receive some penalty (slowness and mining fatigue iirc), but you can avoid it by putting the dolly in a backpack. This effect doesn't stack.

If you upgrade it with 3 diamons you get the Diamond Dolly, which can move spawners but only six times. This is the only tool to my knowledge that lets you transport a spawner across dimensions.

EDIT: Apparently you can use a Bedrock Pickaxe from RotaryCraft to retrieve vanilla spawners too. It takes no damage from doing that, but it's a very endgame item.

I figured it out. When you block select something, there is an option select chuncks. So I just selected a few blocks on each chunck, hit Select Chuncks, and then exported. When you import, there is another crucial option Align chuncks, that will make placing it correctly very easy.