Increase chance of reply when e-mailing an eminent researcher? I found this question, but it does not exactly match what I would like to ask. In my case, it's almost surely appropriate to send the e-mail (since my adviser suggested it), I'm just wandering as to what is the best way to formulate such an e-mail.
The situation
The situation is that there is this bigshot researcher in my field, who designed an experimental framework that is very widely used (which I want to use now). In the paper describing the framework (not so recent, ~2005), he compares 5 (then) state-of-the-art methods, and those 5 are still used as comparison references.
The problem is that, even though implementations for the reference methods are provided, I can not find the parameters used to initialize the method.
It is stated in the paper that the parameters suggested by original authors of the methods are used, but, after weeks of digging through the framework paper, papers introducing the method for the first time, and even trying to guess the parameters so they match the ones used, I still can not get the ones used. Since I want to test the method with slight modifications and not just use it as reference, I can not re-use the implementation provided but instead need to run my implementation with parameters I can not find, and introduce modifications to that.
In short
So, to summarize and generalize: After a few weeks of looking for it, I can not find some parameters used in a (seminal framework) work published in 2005. These parameters are not needed to reproduce the work, but are important in extending it. My adviser suggested e-mailing the author of the paper (who is a well known in the community), but since he is so well know and I'm a lowly PhD student I feel kind of uncomfortable sending this e-mail.
The question
I do understand that this is probably the best (and possibly only) approach to getting the information I need, even if it is not very probable that it will work. With that (and my fear of bigshot academics) in mind, my questions are:

How to best write such an email? Besides the basics (be polite and concise) I don't know where to even start.
Do you have any advice on how to increase the chances of getting a reply? Maybe including my adviser in the CC of the e-mail would be a good idea, indicating my relation to a more established academic?
Your chances of a reply will correlate quite strongly with two factors:


How interesting your problem is.
How long it will take the professor to respond.


Thus, you should:


Make everything as brief as possible, yet still include all necessary information. 
Ask yes, no, or short-answer questions that the professor will know off the top of his/her head. Ask for references to a paper, or for whole pieces of code: not the embedded details.
Briefly mention that you're a PhD student at Fake University, supervised by Professor Jones (if the prof you're contacting likes your supervisor's work, that's a good start).