Your timelines on availability of Pu are off...
Microgram amounts of Pu (from cyclotron production) became available in Jan 1944.
Gram amounts became available in Feb 1944. Hanford wasn't the only Pu reactor - a pilot scale reactor was first built at Clinton (Tennessee, I think), and this provided the gram sized amounts of material.
According to a letter from Oppenheimer to General Groves, as of 31 Aug 1944, 51 g of Pu had been delivered to Los Alamos.
Studies of this metal, and bomb design, had to be completed with these gram scale amounts of material. This was not at all easy, as the metal had some very strange physical properties that had to be dealt with. This was indeed quite a remarkable feat, and understandably perhaps hard to believe, but it is part of the interesting history of this element.
Quantity amounts of Pu from Hanford became available in May 1945. (This date is delivery date, not the start of production). The physical hemispheres of Pu metal for the Trinity test were fabricated at Los Alamos, and completed by 1 July 1945. The physical hemispheres for the Nagasaki bomb were likewise completed by 1 Aug 1945, and then rushed to the Pacific so that they were available for the mass-murder of civilians on 9 August.
Again, this timeline is very short, but remember that this occurred under emergency wartime conditions with the maximum possible contribution from the largest economy in the world.
I got the above dates from the Pu Metallurgy book. I will note that this book has a timeline summary that says the Nagasaki drop happened on 6 Aug, which is incorrect. The Seaborg book describes the same general course of events, I didn't reference it just now to double-check my dates, however.
Another point: Much of the early research on Pu chemistry (on the ultra-microscale) actually happened at the 'Metallurgical Laboratory' in Illinois (I think) where Seaborg was, therefore not at Los Alamos. However, all the work with larger quantities of this element occurred at Los Alamos.