Dude, they got extremely lucky. I'm sure every year they go looking for guys with this profile and it almost never works. They bought low on Eovaldi and he massively overdelivered. My opinion is, don't overthink this. Accept what we found here.October heroics or not, "Yankee killer" or not, Nathan Eovaldi is not a guy you sign at any cost or simply to prevent him signing somewhere else. If he will sign a reasonable deal that fits the budget without financially handcuffing the team down the road, by all means they should sign him. But he's not a guy you need to win a bidding war over.
I don't disagree with the notion of priming the roster for October, however I don't think it entirely needs to be done in December and January. The WS MVP was added in May. Eovaldi himself was a July pick up. Lots of things change over the course of a season. I don't think anyone was looking at the Red Sox roster last winter and saying "all they need is a flame-throwing righty to crush the Yankees" and they're set.
Also the approach you described is reasonable as a long-term plan, but given the way the window is for the current roster, I'm fine with putting the long-term plan at some risk if they can bag two or three titles and then reload.