As far as "Big Week", what you claim sounded "NUTS" was viewed as acceptable losses by Allied Air Command. "lure the Luftwaffe into a decisive battle" sure does sound like they were engaging the Luftwaffe not just HOing and hoping for the best.
"luring" the Germans into battle is some GREAT PR SPEAK (which was an AF priority at that time) which has NO BASIS in reality ... In reality, the germans had been building up their bomber killers over the winter and were intent on clearing the skies of allied bombers in the spring. No one BAITED them into the air.
"Big Week" is well documented since it was an Allied offensive, and yes there was a question of air superiority, unless you think our bombers and fighters only showed up after the Normandy Invasion. 
Allied bombing was going on for a long time before there WAS a front line.
Prior to the invasion, the "Front Line" was the coast ... The germans NEVER controlled the air over it ... The allies conducted tactical raids at will. By D-Day the germans had withdrawn almost all air support to Russia or moved it to rear areas for bomber interception.
Big Week is well documented, but is misunderstood by most ... You probably think the Allies WON ... In reality, we lost around 450 planes to enemy action and they lost around 350 ... Downed Allied Pilots were mostly killed or captured, Germans Pilots had much better survival odds. Close Escort remained in effect during Big Week and saved MANY allied bombers. As mentioned BIG WEEK was what the GERMANS were prepared for. The bombers concentrated on Vital Aircraft Factories, but failed to accomplish much ... due to the INTENSE and FREQUENT interceptions. The ONLY thing that saved the allies was, the suprise introduction of the P-51 in strength.
