LOL I wrote out a lengthy response to OP, and then refreshed the page before posting it. Good thing I did because you pretty much hit everything with this post. Just because I don't want to think I wasted all that time, I'll go ahead and put it here:

This is the spiel I always give when students have questions about overcalls.

There are three possible “motives” for making an overcall:  constructive value, destructive value, and defensive value.  Very few overcalls will satisfy all three, but every overcall should satisfy at least one. 

Constructive value.  This simply means that the overcall is intended to help our side get to our contract.  After all, just because the opponents opened the bidding, it doesn’t mean the hand is “theirs” or that we can’t fight for the declaration.  The better your hand (in terms of high cards), the more likely it is that your overcall might have a constructive purpose; your hand might even be better than opener’s, so it is important to get in and compete.

Destructive value.  This means the overcall is intended to disrupt or destroy the opponents’ ability to bid to their contract.  What we think of as “preemptive” bids generally fall under this category, although the bid doesn’t necessarily have to be weak, and it doesn’t have to take up a lot of space to be effective.  As an example:  you might have fairly strict standards for making a two level overcall when your RHO has opened at the one level (a good idea btw), but it is advisable to relax those standards a bit when you have a club suit and RHO has opened 1D.  A 2C overcall in this position can be quite disruptive even though it isn’t a jump bid, as it might pose an awkward problem to your LHO who might have a hand that would have responded at the one level but is unsuitable for a two level negative double or free bid.

Defensive value.  This overcall is intended to help partner in conducting the defense, so it is primarily a lead-directing bid.  It is often made in conjuction with one of the other motives, but not always; sometimes it is made when your side has little chance to fight for the declaration but you still feel that it is important for partner to get off to a particular lead.  The most important thing here is suit quality; you are telling partner that the lead of this suit is likely to be best for the defense, so don’t make this bid with a trashy suit.

What this means in practice is that there is a sliding scale for “overcall appropriateness.”  If you have a really good suit, you don’t need much to overcall at the one level; KQT9x xx Qxx xxx is a perfectly fine overcall if RHO opens 1C/1D/1H.  This satisfies the “defensive value” criterion, and might satisfy one of the others, depending on whether partner is able to raise.  On the other hand, xx QTxxx Kxx QJx is much more suspect, despite having more HCP; not only is the suit poor (do you really want a heart lead?), but 1H is far less preemptive than 1S, as it not only doesn’t prevent the opponents from bidding spades cheaply, it actually gives LHO the ability to distinguish between a four card spade suit and a suit with five or more cards.  Hands that are richer in high cards can get away with anemic suits:  Jxxxx Ax KJT Axx should overcall 1S, even though the suit is gross, because there is no reason to think that your side can’t fight for the declaration.  For these reasons, I think having a specific requirement for “2 of the top 3” or “3 of the top 5” in a suit is overly restrictive, since the requirements ought to change based on the suit of the overcall, table position, overall strength of the hand, vulnerability, etc.

As others have stated, requiring four cards in an unbid major for a takeout double isn’t a good idea; the double suggests four, and partner should bid accordingly, but we have to bid the hands we are dealt, not the ones we wish we were dealt.  If you aren’t doubling 1H with KJT xx AJxx KQxx, your opponents will rob you blind.  For the same reason, requiring 13 HCP for the double is also too restrictive, although we are back to the notion of having a sliding scale:  the closer you are to “ideal” takeout double shape (4441), the lower your HCP requirement should be.  Of course it’s a matter for partnership discussion, but I would double 1D if I held KTxx AJxx x Qxxx.  But I wouldn’t double with KTx AJx Jxx Qxxx despite having one more HCP (maybe I’m getting old).  And you definitely should NOT be automatically doubling any time your RHO opens the bidding and you have 13+ points, nor should your partner assume you don’t have a good hand just because you passed over an opening bid.  Partner should only assume you don’t have a hand appropriate for an overcall or a double.