I'm not familiar with Jon Meacham, so I'm not sure what you're looking to avoid, and I'm also rather new to the idea of differentiating in the style of non-fiction writers.
That said, this book is not something I can put down with ease. It's rather detailed, and not at all repetitive in language, if that's what you're looking for.
Also, have you seen Tip O' Neill's autobiography Man of the House? I liked it rather a lot. He provides plenty of detail of legislative and machine politics, or at least more than I've seen most politicians willing to admit.
My grandmother is a former member of the Maryland Democratic Central Committee and a life-long campaigner, so she's showered me with more political biographies (and anecdotes) than I can count.