Something that's been bugging me about large portions of this discussion (admittedly, I did this myself) is that I feel like we're getting caught up comparing Amulet to Steward and, to a lesser extent, Jack of All Trades. While this is somewhat helpful for understanding the roles of a card that we're all probably not as familiar with now (not being online and all), I feel its easy to fall into a trap where we think "this card isn't as good as Steward, therefore, something". But knowing that Amulet isn't as good as Steward in engine games or JoAT in money games doesn't help me if Amulet isn't in the supply with those cards. Even if I know that Trade Route < Amulet < Steward, it doesn't tell me a whole lot about how good it is, how many I want, etc in games where the comparison cards aren't there. I know its not intentional, but when the conclusions the discussion naturally lead to are "Card X isn't as good as Card Y in games of type φ", we miss a lot of understanding about the card.
So I don't think I agree with the bolded part above (that the discussion comparing Amulet to Steward and Jack isn't helpful). I think it's very helpful, possibly some of the best discussion that can take place without the ability to actually play games and look at logs/videos. Why?
Well it plays a similar role in those decks, so knowing what you know about Steward/Jack and these comparisons can help you answer those questions you have. For example:
How many Amulets do I want in an action engine if its my only trashing and I never want to gain silvers with it?
If you're looking at a board where you would open double Steward for the purpose of thinning quickly, then yeah you should probably open double Amulet. Maybe you want a third Amulet if you feel like your draws are not letting you thin as much as you'd like (you would have this problem with Steward <3 #stewardisthebest <3) but all I needed to know to get me on the right track is comparing it to Steward.
Pretty much the same argument can be made for your other question by the same reasoning.
What if you wouldn't open double Steward? This means that you aren't concerned with thinning as quickly as possible, so you'd just get one Steward, right? Wait, I don't need your approval for this, I'm making this scenario up. Speak with authority, Adam! Ahem. I decree that on this new hypothetical board you've decided you'd only open with one Steward for thinning! Complaints may be directed to the circular file.
Well the pace of your trashing is less important to you. I'd get one Amulet here, maybe a second Amulet on the second shuffle if you want a little more pace, but I dunno I'm just sort of guessing what would be close to what Steward does.
I know these questions are often context-dependent, but some guidelines about these types of questions would go a long way towards educating players who don't have a full understanding of these nuances and who otherwise will just know that its worse that Steward.
So I hope you see my point that these guidelines are most easily explained by comparing the card to Steward. Steward has been around for like 8 years so that feels like a pretty valid reference point as long as you point out the differences (draw vs. gain a silver, missing shuffles, flexibility blah blah blah).
It's a similar story with Jack, though the last few posts here I think are just a little off in one area: if you're playing Amulet for the same reasons as you're playing Jack (so you have a money focus) then Jack's draw is a really, really big deal and I think that's being underestimated by a lot. You get defense from tons of attacks with this and that draw never stops being good for you economy. I mentioned this before and maybe I didn't say it strongly enough: Jack is much, much better than Amulet for Big Money and possibly even slogs.
This is why I compared Amulet to Hermit for money games, I feel like that's a much better comparison power-level wise. Sure, Amulet is in between Jack and Hermit, but it's gotta be much closer to Hermit than it is to Jack. Like, maybe Amulet is "Jack-lite" and Hermit can be "Lil' Jack"? There's gotta be a pun in here somewhere, like a Lil' Jon reference? (PPE: it's a meme, it's totally a meme. Unfortunately I'm no good at making memes so someone else will get all of the +1s for this. I just hope it gets posted in the meme thread and not here.) I dunno, I don't listen to rap, I'm more of a TSwift fan.
...and as an aside, you can see I made little quips and references in this post but pretty much all of the content was about Dominion. Isn't it a great post? I should get +1s from the quippy people AND the Dominion people!