Get the 360 block from the machine shop and buy a set of bearing spacers so you can use your rotating assembly back. I did not read back far enough to see what bore size pistons you have, but if you bore the 360 to 4.040 you could use stock 340 pistons. There was a NICE set of 10.5-1 factory 340 pistons for sale here cheap a week or so ago. Good luck to you. Check the thread linked below to get the info on the bearing spacers.
Homemade 340 ### | For A Bodies Only Mopar Forum