So how much gear would he need to pump into Darwin for it to be a viable target?
B-17s. "Netties" and Kido Butai can deal away with ships, but there are so many troops and presumably AAA units that I dont want to bomb the airfield with my fragile bombers, and especially not with the well trained carrier and G4M pilots. If, and when, B-17 presence is confirmed, the BBs will dash in, IMHO killing "even" 15-20 of them would be worth the burned fuel, bonus points for hitting the port, any shipping, troops and killing fighters and other bombers on the ground or by Zeros in the air.
USAAF modern bomber losses are now (including FOW but the numbers should be close) 8 x A-20, 68 x B-17, 28 x B-25, 90 x B-26 and 3 x B-24.
I did some research, and by the end of the month he should have had available a grand total of approx 225 B-17 D and E models. That means theres 157 still out there, and 2 months from July 1st he will have received 48 B-17Fs and somewhere around 40 more with fresh units. He should also have approximately 40 LB-30s (early B-24) and another 40 B-24Ds from July to December. To stop their numbers from rising, we need to(or thats what I try to achieve) kill 2/3 of the 225+90+40+40 = 395/3*2 = 263 bombers. We have now killed 71.
Many of those heavy bomber units are restricted to West Coast only but he should be able to free most of the planes to actual front line use... Approximately 50 of them sit at Port Moresby, so he doesnt/shouldnt have more than 150-ish elsewhere, most probably at least 30 of those sit along the West Coast doing nothing.