there's this huge majority that say there's not enough data to draw strong conclusions
Where did you get that idea? In fact, where did you get the figure of 4000 articles endorsing AGW? The original link (Powell's study) makes no mention of that.
Perhaps you're confusing it with Cook et al 2013, which does say that 4,014 of 11,944 papers "expressed no position". Reading the actual study however shows that 0.7% of papers examined rejected AGW and a tiny 0.3% were uncertain about the cause of global warming.
Let me repeat: of 11,944 published papers, 66.4% expressed no position on AGW - they concerned themselves only with a specific area of climate science - and no conclusions can be drawn from them. Only 1% felt the evidence was inconclusive OR counter to AGW. Thus, of the papers that did take a position, including that no conclusion was possible yet, 97% supported AGW.
If you've read "analyses" that claim otherwise, they are being deliberately misleading.
Plus of course the half-dozen other studies over the last decade confirm and verify these results.