This is a really good story, and it drives home the famous @patio11 mantra: Charge more! (Even when you're an employee who charges a company a salary for your work.) This is an amazing success story that drives home the importance of knowing your value and using that knowledge to get paid what you're worth. Very cool :)
Some more thoughts...
Aggression
Your tactics are very strong and aggressive. If you're truly indispensable, this level of aggression can pay off in a big way. Two factors go into figuring out how aggressive you can/should be:
1. How badly the company needs you.
2. How badly you need them.
This seems obvious, but I think a lot of people overlook the relationship between those two things and your ability to negotiate aggressively.
The more they need you, and the less you need them, the more aggressive you can be. In this case, it sounds like you knew they needed you badly and you had many other options and little loyalty to the company, so you didn't need them very much. This is a situation where strong aggression is merited.
Knowing your market value
I especially like that you went and got real offers from other companies. This is the best way to estimate your market value—a key step to complete before jumping into a salary negotiation. If you can find out what other companies pay for your skill set and experience, and if you can determine what your current company will pay for your skill set and experience, you know how hard you can push.
Knowing your minimum acceptable salary
You didn't mention this, but I think it's implicit: It's also important to set your minimum acceptable salary before the negotiation. What's the absolute minimum you will accept in order to take the job or stay with the company? This is your "walk away" number, and it can be a very, very potent tool when you're negotiating. Pre-deciding this number gives you total control over your situation and helps avoid any knee-jerk decisions that you may regret later. Knowing your market value can help set this number accounting for more than personal feelings.
Here are a few more thoughts on things I might recommend doing differently (since I know a lot of people will read your post and hope to emulate your success).
I recommend witholding your desired salary
When you were looking elsewhere for opportunities, you said, "They asked me what my other company offered, and I said $60k (a lie, I added $14k to the original offer). They offered me $58k plus a $7k performance bonus, for a theoretical $65k package." It is not a coincidence that the company's offer was slightly less than the number you told them.
And again when you tell your employer about your other offer: "I went back to my original employer and said I had a new job offer for $70k, and I didn't want to negotiate, I just wanted their final, last ditch offer. This removed any potential for skilled negotiators to outwit me. Later that night they emailed me an offer for $66k and a few thousand more shares." Again, it's not a coincidence that they offered slightly less than the offer you had on the table.
Rather than telling them your desired salary, or what other offers you had on the table, I recommend simply kindly refusing to disclose these numbers. You very likely would have been better off using one of my favorite lines: "I want this move to be a big step forward in terms of both responsibility and compensation."
In fact, your story sort of bears this out. They obviously had a LOT more headroom for salary, and yet the salary you got was always slightly less than you had requested.
I don't recommend lying
A few times, you determined your market value by getting offers at other companies, then went back to your employer and lied about those offers at your company. This worked out for you, but seems pretty risky. Why lie? If they fact-check you at all, you'll be in a pretty awkward position of explaining the lies.
Instead, just don't tell them the numbers at all :)
If you were going to demand their best-possible offer anyway, why not just demand their best offer without giving them an anchor?
I think yours was a special case, but is still illustrative
As I mentioned above, you were very aggressive here, demanding a raise and threatening to leave multiple times. Most people probably cannot get away with this sort of aggression and will end up either leaving or having their bluff called pretty often. (I don't think you were bluffing here, which is why you could be so aggressive as I mentioned above.) I just point this out so those who may want to emulate your succes are aware that yours were very aggressive tactics that may often result in separation from the company or bad blood within the company if managers feel that you will constantly demand raises under threat of leaving.
I'm publishing a book on salary negotiation very soon. You can check it out here: http://FearlessSalaryNegotiation.com