The first P-39s (P-400) sent to the UK were literally some of the first P-39s manufactured, there were some bugs as with any new plane. The problems you mention were soon worked out. The P-39K/L were produced July/September 1942 and were on Guadalcanal by September. P-400s were there from the beginning (August 1942) albeit they were those with the British oxygen system which was incompatible with the Marine equipment on Guadalcanal, so their altitude was limited to 12000'. The P-39/400 was there for combat from the beginning of the war. Over 700 had been produced by Pearl Harbor and almost 3000 were produced by the end of 1942.
I believe you are a little off on combat introduction of the Spitfire IX
Spitfire Mk IX versus Me 109 G - Flight Testing The first squadron was introduced at the end of July and initially only 4 squadrons were in combat. Series Mark IX production began in early 1943 with the introduction of the Merlin 63, 66 and 70. The initial P-47 combat mission was on April 30, 1943 coinciding with the 8thAFs first 100 plane raid. The Mustang Mk I first combat was in May '42 and only 138 had been produced in 1941. The 100 units per month mark was not achieved until April 1943.
The P-39, P-40 and F4F were the only US planes available through almost all the first year of the war. The P-39 and P-40 were the most numerous AAF fighters in the Pacific until September 1943. The P-38 saw combat in late '42, the Corsair in February '43, the P-47 in late April '43, the Hellcat in August and the Merlin Mustang in late '43.