My max deadlift is 350 (still gaining), but I can deadlift 300 twice. Is it better to focus on my 2 lift max or my single lift max to build overall strength?
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I don't think there's a big difference between doing 2x and 1x. Both are focusing on the extreme of strength. I personally prefer to do 1x just because the higher weight (compared to 2) boosts my ego, and removes any ambiguity when I want to calculate set weights based on my 1 rep max.
That said, you'll probably do better to apply stimulus in something more like the 4 rep range, and just use 1 or 2 rep sets to test your progress. For example, my current weekly (well, I use an 8 day week to get 2 days of rest between each cycle) workout (based on the Texas workout described in Practical Programming) is this:
In a schedule like this, you can alternate 1RM or 2RM on the last day. A reccommendion in practical programming was to alternate 1 and 2 every other week.
I would stick with novice programming on this lift for now. A 5/3/1 might work, but I think it would be more efficient just to focus on making linear progression work.
If your max deadlift is 350, it doesn't make a lot of sense to worry about your 1 rep max (1RM) or 2RM. At that stage it's more productive to focus on your 4RM or 5RM. You want to focus on building your strength and power with heavy sets of 4-6 reps, not demonstrating it in a max single. This is also much less likely to cause injury, and easier to recovery from.
A 300 pound 2RM deadlift is still well within the range of linear progression. Weekly or twice-weekly sets of 5, adding 2.5 or 5 pounds each session or every other session, should be feasible if you're getting enough rest and eating enough.
I'll be double-checking pages 79-82 in Practical Programming later to make sure this makes sense (per Starting Strength forums).
Practical Programming's Answer: 1-3RM For Strength
From page 79:
Notice that in this context, Rippetoe is using a narrow definition of strength that does not include power, hypertrophy or endurance. Doing fewer reps and only one or two sets makes for a drastically lower volume and average load at the limit of your ability (I'm paraphrasing from the second paragraph on page 82 there). For these reasons (and the increased danger of injury), I would recommend against using 1RM or 2RM as regular training stimulus.
Though the original on page 60 of PP is better (the gradations from range to range are less stark) this chart from reddit does an excellent job explaining the effects of different rep schemes:
Rippetoe's Reasoning For 5RM Instead of 1-3RM
The key line for you is from page 102, emphasis mine:
It's very possible that you still fall within the novice range of your potential. If that's the case, deadlifting sets of 5 instead of 1 or 2 would be optimal for overall development. If you've found that you cannot progress with daily increases, or that the 5RM is too taxing despite eating and resting sufficiently, working with sets of 2 or 3 in the deadlift could be better.