As a person that many people want to get in front of, I can hereby certify that this fellow would have been blocked by a bayesian spam filter by email #2.
The trouble here is his attitude. It's all about demanding and demanding and demanding. Gimme. Gimme some time. Gimme some attention. Then gimme some mentoring, gimme some money, gimme an investment. You know what? Ef you.
The solution to landing meetings with anyone you want is fairly easy and has been understood since Dale Carnegie explained it (http://en.wikipedia.org/wiki/How_to_Win_Friends_and_Influenc...) in 1936.
You have to stop demanding things from people and start doing things for them.
Comment on their blog posts.
When you find out they have a new puppy, mail them some homemade puppy treats with a nice note.
When they ask a question on Twitter, move mountains to find an answer and send it to them.
Find out what charities they work for and make a donation. Or volunteer.
Write a blog. Give freely of your own knowledge. I did that and went from anonymous to internet-famous in 2 years. When I wanted to raise money, everyone knew who I was, and I got meetings with anyone I wanted with a one sentence email. Not because I was lucky and not because I was blessed and not because I was in the right club, but because I had been making a contribution for years before I started demanding things.
Either you're doing something I want to know about or you aren't. Don't give up after one try but don't bug the person constantly either. If they're not paying attention maybe you aren't interesting.
To follow up on some of your points: I don't know how easy it would be to get someone's mailing address--in my case, even getting their e-mail address correct was difficult. It's definitely possible to help them with something on Twitter or comment on their blogs, knowing that it takes a bit longer--and you have to wonder, at what point do you make the ask? You can compliment and help someone for a while, but at some point you have to ask them what you want to ask them. I'd be interested in hearing how you transition from being nice and giving to asking.
The problem with my own advice is that it's public in a large blog that is read by lots of people. This is exactly the same advice I'd give to any person who came and asked me "There's this investor, he's perfect for what I'm doing, but he isn't responding to my e-mails for the past 3 months." I could see people skipping that first part, which I would not do--you can't just start off by saying "Hey I'm going to e-mail you every day for the next 30 days." I sent nice, well-thought e-mails (VentureBeat edited out that part because the original post was too long) and got no response. Everyone who agreed to do the interview enjoyed it though. If I'm trying to get your attention, it's not like letting you invest in my company is only going to benefit me, remember I'm going to make you rich(er) some day! At least that's what I think, and that's what you're betting on when you invest.
I doubt I'll ever see a busy person support this advice openly. This is mostly targeted to the few people out there who are trying everything and it's not working. I'd use a combination of what you've suggested to build up some rapport, and eventually do what you could (using this tactic) until you're satisfied knowing you tried everything you possibly could before you quit and give up. I can't sleep at night knowing that I could have been just a little more persistent, but I gave up instead.
I have people doing what you suggest to my mobile phone. They call every day with a recorded message offering to solve my "money problems" and telling me that the only way to get them to stop calling is to give up and talk to them. If I could control the policies on my mobile phone the way I can on email, I'd send their calls straight to the trash without passing through me, as I do to anyone who attempts your suggested email spam strategy. I can't recall any case of someone successfully spamming me into submission.