Playfield swaps are no doubt intimidating at first. It looks like a very daunting task. Sliding the underside onto a piece of cardboard is a good technique...used it once myself. The one thing you'll find, though, is that the harness tends to keep everything in place. Personally, I think it's easier to get everything loose, then get another person or two and everybody grab a portion of the harness, pick it up and move it to the new playfield. You might even find you could stuff the whole thing in a box -- like while you're restoring your playfield -- and when you pull it out and lay it back down and get a few points back in place the rest of the stuff is right where it's supposed to be.
I equate it to doing a puzzle. Yes there's lots of pieces, but don't feel you need to do it all at once. Every time you have 10-15 minutes go screw a few things down. Screw down the harness clamps, or a pop bumper nest, or a group of lamps, or staple some of the braid down. Just pick away at it little by little and you'll realize it's not as intimidating as you once thought.
THE most important thing is to make sure you use the right screws on the right part. It's all too easy to grab a screw from one of the mechs and use it to screw down a lamp socket only to find you just ran it through the top of the playfield. For my first swap I would grab a couple of bins with divided compartments and keep all of the screws separate. Drop target bank screws, pop bumper screws, lamps, slings, etc. all in their own compartments with notes. Inspect everything and question it here if it looks wrong. Check and double-check before you screw it into the playfield.