I think you are being perfectly reasonable. On the other hand, I would be feeling a bit like you are "Oh gee, are they going to blame me or think I'm too picky?"
Okay, look at it logically. It's Apple who should be feeling bad (I mean, if anyone were). They sent you three DOA computers. That has cost you untold time, lost use of computer, stress, etc. Granted, they did not do it on purpose, and they are making it right, but I'm just saying shoot, that should not count against YOU. YOU did not manufacture 3 defective laptops. Again, it's not Apple's "fault" either, in a malicious way, but if anyone should be embarrassed it should be them not you.
And in another way, those three other computers don't "count" against you now. Now it's THIS computer, and it's THIS computer you just "bought" new. If this computer is not "like new" then.... I would exchange it. Like someone else said, you don't buy a new car that's all dirty and scratched just because it will be that way SOMEday. It's up to you to get it dirty or scratched (or not) as you see fit.
Now if it did not bother you, fine; but clearly it does. It would me too.
So, if it were me I would just grit my teeth and make the call, and just force myself to be calm, to state what happened and what you would like to happen now, and then let them handle it. If they are not giving you good customer service, just repeat what you would like, and/or ask to talk to someone else.
Technically, you could just RETURN the computer, no? I mean, it is less than 14 days old. So you are asking for an exchange, but you really could just return it and buy a new one (unless policy is different where you are).
You mentioned the UK store and that you will be there soon. You know what I would be tempted to do? See if they will let you pick up the new one there (if the keyboard is correct for you?), and then you can open each one and check it out, and if there is a problem simply hand it back to them. Or, return what you have now and buy a new one in the UK (again, if the keyboard is correct).
At any rate, you sound like someone who can talk with Apple customer service in a rational and polite way, so call them up, let them know how much you appreciate their great customer service, and then let then know why you need it again. Heck, by this point I'd be asking for free Apple Care or SOME perk. Not to be greedy but you have spent hours and hours of your personal time, and you have been without a working computer for WEEKS after you paid full price for it. You can bet no business would just give you their time and weeks of computer use for free; well, your time is worth something too. I wouldn't push that aspect of it, but I don't think a polite query is unreasonable.
Good luck and I'm sorry you have had so many duds!
Miss Terri