Recently I have been working with a complete beginner to not only pua but talking to people in general. So I've come up with what I believe is a new method for overcoming approach anxiety at a very low level.

Basically with the support of a friend or on your own (friend is preferable for support but not essential) you walk around town or a mall and instead of the usual method of just saying hi which is quite a daunting task for a beginner, all you do is ask the time now this can be men and women and incurs no repercussions if you mess up. By doing this for about half an hour the results were incredible and so was the progress. However the main things to remember when you go out there and try this are; stand up straight, keep your head up and mystery's number one rule always SMILE.

However I am yet to progress this to the next stage in this method. I'm thinking of slowly building on the interaction by adding an opener instead of 'excuse me, do you have the time.' I would probably use an opinion opener. Also a great tip if you feel confident enough asking about an accent is a great source of conversation as i found out in the field earlier. Anyway if enough people are interested in this method I will post a follow up on introducing openers into the 'What's the time?' routine.

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Leave her better than when you found her...

I find your suggestion a bit odd. Asking people "what's the time" is way more annoying than saying "Hi" to people. Like all people can do when you say "Hi" is to say "Hi" back, or just to walk on. However, when you ask people "what's the time" they are forced to reply you, and annoyed by the fact that you don't own your own watch.

Also "excuse me" is good manners, but those two words can set you up for immediate rejection...

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"Everything you do will be insignificant, but it is very important that you do it" - Gandhi

It's good in principle, but not execution. The previoius poster pointed out the reasons why.

Better would be to ask each person something specific to them in that particular circumstance. Like a mix of observational assumptions and spontaneous approaching. For instance, walk up to a guy/girl eating an icecream cone. "What kind of icecream is that?" Then instead of asking is it good, where did you get it, how much was it, etc., you make some sort of witty joke about it.

You're trying to get people to overcome AA just by saying words to people they don't know. But I think you can make it a little more complex than that. Make them work a little harder and be a little more uncomfortable, even in the very beginning. And if you're there, you can tell them what to say initially when they approach, then leave them to small talk once they open.

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“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn

The main idea behind it like you say is to force an interaction which is exactly what you need if you struggle talking to people. It is by no means a full on pick up technique like an opinion opener it is just to boost the confidence with the idea of building on what you say the important thing being that you do approach.

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Leave her better than when you found her...

you know what, the "what's the time" routine always works for me..

every time i enter a public jeep or bus i always look for a target chick then sits close to her. i'll ask her the time, most of the time they will show me their watch and seldom choose to talk. .. the great move here is to hold her wrist and look at her watch as if your a nearsighted. the touch should make her feel that your confident,. after, i'll ask if her time is in advance or late, she will answer ofcourse.. and i'll follow up with some other questions like "where do you work? i think i saw you at *** before". the real key here is to SMILE everytime u ask.

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honesty is the best policy

I've done that when I just began, and it worked for me. I find that the problem with the "Hi" openers early on is that people often give you weird looks and, if you have problems with inner game (which your friend obviously does), it will shut you down very quickly. If you ask for time, however, nobody will look at you as a weirdo, so it's a much less painful start.

One thing to do in this stage is trying to push your comfort zone (strangely enough, there is one even for that). I walked around the streets asking people how to get places, but I found that talking to groups of people, to hot girls or to people that seem to be busy is harder than usual. So by talking to them you learn to overcome your fear.

Another thing I found out is that the comfort gap between this and opinion openers is too large. By asking time or directions, you are asking for a service that everyone is willing to give in this society - and you know it. However, asking someone's opinion on something seems very illogical to most people (you don't even know them, why would you care about what they think?).

So in that case, I would try to find some smooth way to go into a story. For example, in your case, if you're walking in a mall you could do something like:
You: Hey, what time is it?
Her: 5PM
You: Oh, ok (think for a second). Do you know if Madagascar is still playing? Cause me and my friend went to watch it yesterday, but they accidentally screened Paranormal Activity 4... blablabla (or whatever BS u'll come up with).

It practices story telling and shows your friend that people are willing to listen if you smile and say interesting stuff.

I think the use of the words 'since I'm talking to you can I get your opinion on something?' would work well after 'what's the time etc'

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Leave her better than when you found her...