OK - I'm going to take this in another direction. How about instead of finding a best argument strategy for this year's raise, you figure the best way to harvest information out of your manager for next year's - so you know what he really thought you could do better, and you and he start agreeing on what "better" looks like?
I say this, because while you may find a way to game the system up or down a notch, the real key to making more money in the long term is simply doing better work. If you walk into the meeting as a real all-star, you won't really need to worry about whether you go first or last - you'll know that your performance review will be a big "atta boy!" and it'll be followed by hopefully some good money!!
On the fly adjustment
Having been a low level manager in two organizations, I'll say honestly that changes (even very small ones) in a performance rating was NEVER something I could do on the fly. When I had to provide the manager-review part of the performance review, I have always had to vet those ratings back through an organization, as almost any organization with more than 1 manager in it needs some way (always rather flawed) of level setting so a tough manager doesn't thrash his people while an easy to please manager gives everyone super awesome ratings. So - my serious bet is that if the manager can truly change that 1 single important number/rating that means serious money, then you have a very, very rare case on your hands -- at least among a large, somewhat formal, organization.
My strategy here would be that honest feedback giving from manager to employee is tough. I don't know a single manager who is perfect at it - we all have flaws, and for almost everyone it's also emotionally exhausting. Being fair, clear, honest and specific about an employee's shortcomings is hard work, and most managers are not well-versed in it or well practiced, and very very few were promoted to technical management because they were good at this part of the work (most are good at something technical).
Your single best advantage to play here is to find a time when you can maximize your manager's ability to give you honest feedback. IF you go in there to "sell" him in your skills instead of having a meaningful discussion of how you can better maximize your contribution to the organization, then you are missing out on a real opportunity. Having just had to sit down and go through the process of rating and evaluating everyone, your manager is in the unique end of year position to be clear and honest about what's good and what's bad, and why it matters so much. There's nothing having to brutally compare and defend people's ratings to make a manager far more thoughtful about this than he might be at any other time in the year.
Getting the Meeting you Want
So, if what you really want is to do better and get more meaningful feedback about your work and your potential growth in the organization - here's my thought on a strategy:
Head for the middle - don't be the first where your manager is still getting warmed up for the year in the process of giving feedback (doubly true if this is a new manager who hasn't done this before). Don't be last, as your manager may now suffer from feedback overload and may be too worn down to be insightful or eloquent.
Make notes as you do your part of the review. When I do these, I usually hit on points where I don't really know whether a given aspect of the work was bad or good. Make a note and ask. Also have a thought as to anything you feel particularly strongly about, where it would be a shock to you find out your manager felt completely different. Those are the two areas you'll want to make sure you clarify with your management.
Plan a time when you can accept the feedback. If you think that it'll hose your weekend or make a bad Monday even worse, then head for a time when you think you can welcome and hear constructive criticism. Similarly, if you see that your manager seems to be in his best form in the morning or the afternoon - try to find a time that will work for both of you. Some of my best managers for this have pushed back when I've tried to book the meeting between too many other things in their schedules, because they were smart enough to know that they needed time to prepare.
Get your side of the review to your manager a few days (but not 2 weeks) before the meeting. Enough time to read and prepare, but not so much time that the manager can totally forget it came in. Obviously mileage varies in corporate rules and so forth, but in general, dropping a performance review on your manager's desk an hour before your meeting to go over the material will almost always get you low quality feedback - it's just not enough time to actually form meaningful thoughts.
Have a wish list - if you could do any new work, or any job in the company - what would it be? Why? What makes it a good pick for you and what draws you about that work? Have this in mind so when the review feedback is slim or lacking, you can talk about what you'd like to do next year, and how you can grow yourself to be able to take on that work.
Never let negative feedback go unsupported by evidence or examples. You don't have to be defensive - but asking calmly "can you give me an example?" or "what's the reason for this concern?" if you aren't told is important. Never the manager get away with vague statements you don't understand. Granted, mileage varies - if your review is very positive, don't nitpick the one negative piece of information - instead return to step 5 above. But it's all too common in a negative case for the manager to think he's being clear and for it to be completely unclear to the employee.
Sorry that this isn't a "how do I make my rating be different" answer - in all honesty, if your organization is working well, there should be enough checks and balances in place that gaming the system is harder than changing your behavior to meet or exceed expectations.