I agree that recommendations and your recent work weigh more heavily than bad grades in your past.
I personally would not address your past grades at all- your cover letter or statement of purpose needs to be short, clear, and positive. The applications committee will read hundreds of these things, so you want to do everything you can to get thrown into the "possible candidate" pile rather than "reject" pile. Let them worry about your grades when they go over your transcript with a fine tooth comb, not as your first impression. If your letter talks about your accomplishments and preparation, and your recommenders back you up in this, then I doubt your past grades will need any explanation.
If anything, you could work an apparent explanation of your grades into your cover letter without ever calling out your past explicitly. For example, "Once I discovered particle physics I knew I had found my calling." There are plenty of academics who did not have stellar grades.
Different schools have different policies on grades and minimum cutoffs. I can tell you that I personally did not meet my graduate school's minimum cutoff for GRE scores (by just a few points). The admissions department swore up and down that I could never be accepted, but the admissions committee in my department thought I was a good candidate and accepted me. Your experience will vary.
In general there are two kinds of people on admissions committees (or maybe, two kinds of processes). The first kind of person is looking for reasons to include candidates and pass them along to the next level. The second kind of person is looking for reasons to cut or exclude candidates from the next level. You're never going to satisfy that second kind of person unless you have perfect grades and impeccable credentials, which most all of us (including in academia) do not. Also in my experience you're not going to enjoy working for that kind of person either. When you sit down to write your application packet, think about that first person who is looking for good reasons to pass you along for the next round of consideration, and write with that person in mind.