I wrote this trying to figure out a way that this ruling could work. I don't expect it to make any difference, but here it is.
This is somewhat similar to chipperMDW's interpretation.
The main problem lies in figuring out "when would" abilities, which are actually very strange. First of all, the whole concept of several abilities triggering at the same time and then resolving consecutively is strange in itself, and not in line with physical reality. In reality, if several things happen as a result of something, they happen at the same time (very simplified of course); there is no mechanism that makes any of them wait. So it's an artificial (but of course necessary) game concept that we make the rest wait while we resolve one. This creates a logical problem with "when would".
Let's start with Trader 1E and Possession. Let's say we gain a card with Ironworks, and we resolve Possession first.
It would seem that when we resolve Possession in the "when would" window, the other player gains the card. Afterwards (after the card has been gained) we would still be in the "when would" window, and Trader would fail. This does work as intended. But now we get to the actual "gaining" step, and we would have to say that it's been cancelled by Possession. This is probably not the intended meaning and not how most people think it works. Rather, Possession changes the whole "gaining thing" and then Trader fails to change it, and THEN we resolve whatever it has been changed into.
So then, in the "when would" window, all we do is change a future instruction. We're not changing Ironworks's instruction of course. Ironworks says to choose a card based on certain criteria, and then gain that card. We now have an instruction from the game, a "meta instruction", which is the same instruction that Ironworks had, namely "gain that card". In the "when would" window, that meta instruction can be changed. Possession changes "gain that card" into "the other player gains that card". It's still the meta instruction that we're set to follow when we would normally "gain that card", but now it's different. Trader now tries to change it, but can only change it from "gain that card". Then we follow the meta instruction.
So how do Ways and Enchantress work?
We have the meta instruction "follow the card's on-play instructions" that we're set to follow at a certain time when playing a card. In the "when would" window, the Way rules change that meta instruction into "follow the Ways's instructions".
First of all, cards like Moat and Harbor Village cannot look at simply what we get from playing the card, since that would include all abilities that trigger from that (tokens etc.). They're supposed to look at what we get from "what the card does when played", but this of course means "what we do when playing the card", so we're back to the wrong thing. Saying "what the card instructs us to do" would eliminate the unwanted abilities; but it would only include the card's instructions and not the changed meta instruction. So we have to interpret Harbor Village, Moat, etc., in a peculiar way: They look at the instructions that we follow as a result of the "follow the card's on-play instructions" meta instruction we follow as the normal step of playing a card, but also if that meta instruction has been changed into something else.
In this way, Ways and Enchantress actually work just like Trader 1E and Possession: They change a meta instruction. Note that Reckless does not do this. It could: we could decide that it works like Chameleon, triggering on "when would" and making us resolve the card's instructions twice instead of once. That would change the meta instruction "follow the card's instructions" into something else. But per the ruling, it triggers during our resolution of the card's instructions, making us do something. It's not "when would".
Anyway, the weirdness here is not Ways and Enchantress, it's that Harbor Village etc. look at the changed meta instruction. It would be simpler and more straighforward if they looked at the card's instructions, that they expected the normal meta instruction to happen, like most things in Dominion expect. For instance, a played card expects the normal meta instruction of "put the card in play" to happen, and can't be moved from any other place. That's because of a specific rule of course, but you'd expect that an ability looking for "direct effects" of a played card would follow a similar rule, that the default meta instruction were expected.
Also, this makes Harbor Village etc. inconsistent with Ironworks. Ironworks looks at "that card" (the card that was chosen and gained), which certainly doesn't exist if Trader was used, so that's perfectly fine. But if Possession was used, the meta instruction is "the other player gains that card", so Ironworks (if it worked like Harbor Village) should be able to see the card. But Ironworks expects only the default meta instruction, while Harbor Village etc. don't.
In this interpretation, Ways/Ench are not interpreted as behaving differently than Trader 1E and Possession. It's sufficient to interpret Harbor Village etc. in the described way. Is it possible to interpret Ways/Ench as "attributing" effects to the card in a special way (as Donald X. has been suggesting) and have Harbor Village etc. be more in line with how for instance Ironworks works? We would have to add a rule that the meta instruction that Ways/Ench create counts as the "default meta intruction" that HV is looking for, meaning that when HV looks for effects from "following the card's instructions", it recognizes "following Way/Ench's instructions" as the same. This is simply the same as my earlier idea, having a rule that "following Way/Ench's instructions" counts as "following the card's instructions". The implication of that is that using Chameleon on an Enchanted card would give +$1 and +1 Action. (This still seems like the best ruling to me.)