The Packing Tape mod allows you to move entity blocks like chests, machines, and even spawners without disturbing any of the contents! All you need is the tape and paper in your inventory and shift+right click the block to pack it up.

Once packed you can break that block and move it anywhere you want!

The contents will stay packed inside so you can even store these blocks for later use. Otherwise you can move to the desired location and place it down.

Then remove the packing and access what you need!