So, I think this is a place where you have to accept that the mechanical text isn't neccessarily going to represent the fiction with as much accuraccy as, well, the mechanics.
The way I've understood it is that, if after 4 days you've successfully made the item, one of two things happen.
1) If you decide to finish the item, we retroactively retcon that you bought the full materials 4 days ago and have therefore had enough materials all along to complete the item, or
2) If you decide to work another 4 days, then you only ever bought half the materials of the item and have been working longer in order to make do with what you have and stretch your resources.
So even thought the text says that you only gather half your materials in the initial 4 day crafting period, I think you can't take that mechanical text as 100% representative of the fiction, unless you can find a way to justify using up the other half of the materials in one day (spending the other half of material cost to finish the item on day 4).
However, now that I think about it, you probably can!
If you wanted to be more faithful to the rules text, you could probably just say that the character uses the other half of the materials as part of the 4th day finalization of the item; just beacuse it took 4 days to use up half of the materials doesn't mean it would take 4 days to use up the other half. Two reasons for this:
1) It's only half the materials in the monetary sense, not pure weight sense. So yes, the first half of materials might be 4 iron ignots, to make a sword, but the other half of materials might be the leather of a rare beast and a strange gem to be used for the handle wrapping and pommel respectively. Applying these componeants wouldn't take as long as forging the ignots, but they would still account for half the item's price. Speaking of time,
2) It takes less time to apply the second half of materials than the first half. So, we might use 4 ignots to make the frame work of the shield, which takes 4 days and involves ardous work, but when we're done with the shield's skeleton, we can either spend 4 more days scavenging the scrap left over from the first 4 day process to finalize the shield, or we can buy 4 more ignots worth of iron sheets to quickly finalize the process. (It's just an example, I'm not a shieldsmith!)
The examples are meh, but I think the principles still make sense and hopefuly that comes across.
But that's just my opinion. Both justifications make sense to me, but that doesn't mean they have to make sense to you, if you disagree. :)