The way I bind multi layers of plastic Nick is to do them all at once. Admittedly you have to work quickly as once the glue starts to soften the plastic it doesn't take long to effect a bond! Cut many many bits of tape and hang them from the edge of your table/bench, the last thing you want to be doing is farting around cutting or tearing off bits of tape halfway through a run!
You'll want to do the body in sections too, neck to horn, horn to mid lower bout, lower bout to opposite lower bout, lower bout to horn then horn back to neck.
Start from your neck end. Lay out your binding on the bench beside the guitar in the order you want it. You want to be able to grab it all at once and not have to muck about putting the combinations in their right places.
This is where it starts to get hectic so make sure nothing's to get in your way once you start and that your tape, that now waits on the edge of your bench, is within easy reach.
Put a short run of glue (about two inches, 50mm's worth) at the start of each layer of binding/purf and roughly put them together into your 'stack' then put a bead of glue in your binding channel (and on the purfling ledge if you are using the smaller height of purf) around to about the horn area (so that the binding/purf is always coming
off and away from the body rather than into the body), quickly place your now gluing binding stack into the channel and tape the start tightly to the body.
This next bit would be better showing you as a video but I'll just have to go with words unfortunately

begin, using a thumb on top of the stack and your index finger on the face, & run your fingers away from where you just taped, pushing the stack into the body as you go. The beads you put on between the strips before, will now run along each strip as it gets 'pushed ahead' of the closing joint thereby gluing each strip to it's neighbour. Once you've gotten around that tight 'internal' bend of the horn, apply tape tightly to what you've done.
Once you get around to the external curve of the horn (and where the channel glue runs out!) put a piece of tape, fan out the unglued strips by placing a finger in between each layer and apply more glue to the sides of the strips, this time put a slightly longer run on because this lot is going to have to last until you get to the lower bout. Once you've done that put a run of glue into your body channel up to the mid point of the lower bout (so that when you've completed this section the strips are hanging away from the body, so it's easier to apply the glue) and repeat the squeezing and running fingers along trick. The binding may come away from the body but don't worry too much as it's the glue that we want to be spreading more at this stage. Once you've gotten to the end of your glue run go back and pull everything back into the body channel with your tape (bind as normal in otherwords). Tape at end of the glue again so it holds the binding in the glue. Cut more tape at this time if you think you're going to need more.
The rest is just a continuation of this process. Bob Benedetto shows this process off far more eloquently in his video/DVD "Making an archtop guitar" than
I can explain it here, so if you know of somebody with a copy try and get hold of it, otherwise you could be stuck with my rambling explanation

.
The more you do it the easier it gets but you may want to have a few dry runs to start with just to make sure you have your process down pat, the last thing you want to be doing is messing about when there's glue on your plastic.
You'll also want to leave the binding/purf stack taped up for preferably 24 hours before scraping flush as with that amount of glue about it would have softened the plastic quite a bit.