I would be looking for a replacement rather than a rebuild, as its probably a darned site easier to find a breaker.
There are some sites that will let you send a query to several sites at once; 'breakerlink' is one name that I remember, but I can't really make a recommendation, not really having used them for anything oily, or difficult to deliver. Anyway, the competition aspect seems to work in your favour, in this case.
Mate of mine just bought a full car for £104...
Not sure that could eat a whole one...but that's cheaper than a couple of drop links, for example...
Either way though, you have been unlucky. I would be tracing back over my steps, see if there is any sign of oil where I previously was. If you see patches of oil, you can contest that you let it run dry because of a failure which resulted in the sudden loss of all oil. Which would certainly be covered by your warranty.
Essentially, if the oil came out pretty suddenly, it doesn't matter if you were checking the oil weekly or monthly, it would have still gone in between oil checks (unless someone thinks that the oil is suddenly vomited out while it is sitting still on your drive, just while you are checking it, and while it is switched off - that seems incredibly implausible, but it is what they have to be suggesting, if periodic oil checks are going to catch it, just as it happens; otherwise you'd be driving it when it happened, and then you've got the same situation as you have now). Its better if you can say 'look, there is the hole it came out of', but if it is clear that it was sudden you should be off the hook.
I'll also go back to the oil warning light; I'm still surprised that you didn't see that come on. If, for example, what has happened is that the oil pressure light has been disabled (eg, because it had a habit of coming on, and the person who sold it to the garage didn't want that to show, and it had been that way when the car was sold), you should also be off the hook, because they sold the car with the 'safety feature' that made this unlikely disabled.
(The 'oil light' is a low oil pressure warning, and you would expect the oil pressure to go low before everything failed. In fact, in the short term, you could argue that, if the oil pressure doesn't go low, the engine should keep on running, although that might be a bit difficult if the car is being thrashed. But the likeliest is that the oil pressure light flickers before it gets irretrievably bad, as the oil level goes low, and the pump has difficulty picking up oil.)