When you use Way of the Sheep, you are certainly following Way of the Sheep's instructions.
The thing is, that definition doesn't match your conclusion that Smithy "does what the Way does". The other definition ("with Way of the Sheep, when playing Smithy, you get +$2 from following Smithy's instructions") does match that ruling. I still don't see a third option; this has been my point.
I've been trying to find the disconnect and I'm wondering if you're maybe missing a noun in your mental model; it doesn't have a great name, but it's this thing (bolding mine):
If we look at the natural reading of the sentence, “it” seems to be “the playing of the attack card”.
Harbor Village is referring to that play of the card; further plays don't interest it.
Reckless's extra follow-instructions is part of the play of the card.
Yes; Reckless looks for a play of a card causing its instructions to be followed.
Let's call this not-well-named thing an "Instance of playing a card." When we talk about what a card does, we're really talking about what an Instance of playing a card does. Each Instance of playing a card causes a sequence of instructions to be followed. Whatever
directly happens in those instructions (i.e. not things that are triggered because of abilities set up elsewhere, so no +$1 Token or Priest) is what that Instance of playing the card "does" for the purposes of Harbor Village, Moat, etc.
When a card is played normally, the sequence of instructions followed in that Instance is the one printed on the card. When a card is instead played "using" a Way, the sequence of instructions followed in that Instance is the one printed on the Way. That doesn't change the card's instructions (no card was shapeshifted; Smithy's instructions are still +3 Cards), but it changes
which instructions are followed.
I think a key point here is that it doesn't matter
where instructions are printed. It matters
what is telling a player to follow them. Like, in your recent example with Priest, the reason the +$2 is coming from "Priest" instead of "Chapel" is
not specifically because that instruction is printed on Priest cards; it's because a prior Instance of playing Priest is what told the player to follow it. By contrast, with Way of the Sheep (or any Way), it doesn't matter that the instructions were printed on the Way; the Instance of playing Chapel really is what's telling the player to follow them.
Or, more simply: Priest's +$2 is triggered; Way of the Sheep's +$2 is not.