This is possible however would require editing region data in your minecraft world. It is possible using something like NBTExplorer to copy and paste the compound tag containing all the data about the entities from each chunk into the same chuck in the new world. This would require you to manually copy and paste each chunk's entity compound tag into each chunk of your new world but if you are willing to do that then here is how you would go about it.
First you would need to download a tool for editing the NBT data in your world. Personally I use NBTExplorer which you can download here
Once you have downloaded an editor open up your minecraft saves folder inside the editor. Then you will need to navigate to the chunk you wish to copy. For instance here I found the chunk at 0,0 and have opened that.
Then you will need to navigate to the compound tag which contains the entity information and copy it as shown.
Then navigate to the same chunk on the new world and paste it as shown.
Finally the new chunk should look like this if all worked. The process will need to be repeated for all chunks that need copying. You will also need to click the save button once finished.