I'm an extract brewer also. I rather like the idea of fixing the attenuation issue before (instead of

) going AG. You may still end up with the same issues. You
may make a more fermentable wort, but the job of turning wort into beer is up to how you handle your yeast and fermentation process, and that ain't gonna change when you go AG.
One thought- when you are oxygenating your chilled wort are you letting the oxygen bubble
gently into the wort? If you do it too vigorously you may just be sending the O2 right through the wort and into thin air. Slow it down and go for 2 minutes.
Also, the higher percentage of dark grains in your grist, the higher your FG will be. And big beers with really high OG's will also tend to finish a little high. But you did say that your problem batches tend to taste too sweet.
Several people suggested subbing out some extract for sugars. Personally I would only ever do this if that ingredient is appropriate for the style. Yes, sugars are more fermentable than malt extract, but is that part of the flavor profile you are after?