As promised, here's how things went, including the rolls that happened after J/F '40:
Here's how the US Entry chits played out:
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I'm sorry if this is somewhat confusing. I trimmed away pretty much everything that had nothing to do with US Entry chits.
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S/O '39
US Entry chits at start:
2 x Ge/It (2588, 2912) - 4, 4
1 x Ja (327) - 1
Impulse 1:
Germany DOW Poland (CW); USE-5 (+1 chit, 1699) - 2 (2, 4, 4)
Japan aligns Siam; USE-7 (no chit)
Impulse 2:
CW DOW Germany; USE-9 (-1 chit, 1 of 3 [0]) - 2 (4, 4)
USSR occupies Eastern Poland; USE-10 (no chit)
Impulse 3:
Italy DOW France; USE-3 (+1 chit, 1888) - 3 (3, 4, 4)
Germany DOW Denmark (CW); USE-1 (+1 chit, 2787) - 4 (3, 4, 4, 4)
Germany DOW Greece (CW); USE-2 (+1 chit, 1052) - 2 (2, 3, 4, 4, 4)
Germany DOW Netherlands (CW); USE-1 (+1 chit, 552) - 1 (1, 2, 3, 4, 4, 4)
Italy DOW Greece; USE-9 (no chit)
Germany aligns Bulgaria; USE-10 (no chit)
Impulse 4:
USSR claims Finnish Borderlands (Allowed)
USSR DOW Persia (Ja); USE-5 (-1 chit, 1 of 6 [0]) - 1 (2, 3, 4, 4, 4)
Impulse 5:
Germany DOW Belgium (CW); USE-5 (+1 chit, 2523) - 4 (2, 3, 4, 4, 4, 4)
Japanese attack on Tsinan successful, disorganized; USE-2 (+1 chit, 2689) - 4 (1, 4)
End of Turn:
USA draws 1 chit to the Ja Entry Pool (2541) - 4 (1, 4, 4)
USA selects Resources to Western Allies; USE-10 (no chits moved) and Occupy Greenland and Iceland; USE-9 (1 chit moved, 3 of 6 [2]) Ge/It - 4
USA selects Resources to China; USE-8 (no chits moved) and Chinese Build Aircraft; USE-9 (no chits moved) Ja
Ge/It Entry: 30 (2, 3, 4, 4, 4)
Ge/It Tension: 6 (4)
Japan Entry: 22 (1, 4, 4)
Japan Tension: 2 (-)
N/D '39
Impulse 3:
Japan Closes the Burma Road; USE-5 (+1 chit, 2911) - 4 (1, 4, 4, 4)
End of Turn:
USA draws 1 chit to the Ja Entry Pool (548) - 1 (1, 1, 4, 4, 4)
USA selects Relocate Fleet to Pearl Harbor; USE-3 (1 chit moved, 5 of 5 [4]) Ja - 4
USA selects Resources to USSR; USE-10 (no chits moved) and Lend Lease to Western Allies; USE-4 (1 chit moved, 4 of 5 [3]) Ge/It - 4
Ge/It Entry: 25 (2, 3, 4, 4)
Ge/It Tension: 14 (4, 4)
Japan Entry: 22 (1, 1, 4, 4)
Japan Tension: 10 (4)
J/F '40
Impulse 3:
Germany denies the claims by Hungary and Bulgaria
Germany DOW Hungary (France); USE-8 (no chit)
Germany aligns Finland; USE-6 (no chit)
Impulse 7:
Rumania aligns with Germany as a Full Ally; USE-3 (+1 chit, 194) - 1 (1, 2, 3, 4, 4)
Japan occupies Nanning; USE-2 (+1 chit, 355) - 4 (1, 1, 4, 4, 4)
Impulse 12:
Italy aligns Iraq; USE-10 (no chit)
End of Turn:
USA draws 1 chit to the Ja Entry Pool (123) - 1 (1, 1, 1, 4, 4, 4)
USA selects Reopen Burma Road; USE-8 (no chits moved) Ja
USA selects Gift of Destroyers to Commonwealth; USE-9 (no chits moved) All
USA selects US East Coast Escorts; USE-3 (1 chit moved, 5 of 5 [4]) Ge/It - 4
Ge/It Entry: 23 (1, 2, 3, 4)
Ge/It Tension: 20 (4, 4, 4)
Ja Entry: 28 (1, 1, 1, 4, 4, 4)
Ja Tension: 12 (4)
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You can see from this that the Allies tried to avoid doing anything that would remove chits.
M/A '40
End of Turn:
USA draws 1 chit to the Ge/It Entry Pool (88) - 1 (1, 1, 2, 3, 4)
USA selects Gear up Production; USE-1 (1 chit moved, 1 of 6 [0]) All (Ja) - 1
Ge/It Entry: 24 (1, 1, 2, 3, 4)
Ge/It Tension: 21 (4, 4, 4)
Ja Entry: 27 (1, 1, 4, 4, 4)
Ja Tension: 14 (1, 4)
M/J '40
Impulse 1:
Italy DOW CW; USE-2 (+1 chit, 225) - 2 (1, 1, 2, 2, 3, 4)
Italy aligns Yugoslavia; USE-6 (no chits)
Impulse 7:
Japan takes Nanyang USE-2 (+1 chit, 132) - 1 (1, 1, 1, 4, 4, 4)
Impulse 8:
USSR claimed the Baltic States USE-10 (no chit removed)
Impulse 9:
Japan succeeds (attack on Ichang), USE-2 (+1 chit, 290) - 3 (1, 1, 1, 3, 4, 4, 4)
End of Turn:
USA draws 1 chit to the Ge/It Entry Pool (186) - 1 (1, 1, 1, 2, 2, 3, 4)
USA selects Lend Lease to China, +3 Tension, USE-8 (1 chit moved, 1 of 7 [0]) Ja - 1
USA selects Lend Lease to USSR, USE-1 (2 chits moved, 7 of 7 [6], 5 of 6 [4]) Ge/It - 4, 2
Ge/It Entry: 21 (1, 1, 1, 2, 3)
Ge/It Tension: 30 (2, 4, 4, 4, 4)
Ge/It DOW: None
Ja Entry 30 (1, 1, 3, 4, 4, 4)
Ja Tension: 18 (1, 1, 4)
Ja DOW: 0%
France conquered by Germany, USE-3 (+2 chits, 44, 300) - 1, 3 (1, 1, 1, 1, 2, 3, 3)
J/A '40
Impulse 1:
Germany DOW Spain (CW), USE-10 (+1 chit, 264) - 2 (1, 1, 1, 1, 2, 2, 3, 3)
Impulse 9:
All attacks succeed (Madrid attack disorganized, Breakthrough in Suez); USE-10 (no chits added)
End of Turn:
USA draws 1 chit to Ge/It Entry Pool (364) - 5 (1, 1, 1, 1, 2, 2, 3, 3, 5)
USA selects Pass War Appropriations Bill, USE-2 (2 chits moved, 1 of 6 [0], 3 of 5 [2]) Ja (All) - 1, 4
Ge/It Entry: 35 (1, 1, 1, 1, 2, 2, 3, 3, 5)
Ge/It Tension: 33 (2, 4, 4, 4, 4)
Ge/It DOW: 0%
Ja Entry: 28 (1, 3, 4, 4)
Ja Tension: 26 (1, 1, 1, 4, 4)
Ja DOW: 10%
S/O '40
Impulse 5:
Japan DOWs Portugal (CW) USE-4 (no chits)
Attack on Tsinan (Automatic) USE-1 (+1 chit, 319) - 3 (1, 3, 3, 4, 4)
Impulse 11:
Italy DOW Yemen (CW) USE-9 (no chit)
End of Turn:
USA draws 1 chit to Ja Entry Pool (2) - 0 (0, 1, 3, 3, 4, 4)
USA selects Start Strategic Bomber Production, USE-5 (1 chit moved, 5 of 9 [4]) Ge/It (All) - 2
Ge/It Entry: 33 (1, 1, 1, 1, 2, 3, 3, 5)
Ge/It Tension: 36 (2, 2, 4, 4, 4, 4)
Ge/It DOW: 0%
Ja Entry: 31 (0, 1, 3, 3, 4, 4)
Ja Tension: 27 (1, 1, 1, 4, 4)
Ja DOW: 10%
N/D '40
Impulse 1:
Japan debarks GARR into Kwajalein USE-10 (no chit)
Attack succeeds (Kweilin), but units disorganized USE-2 (+1 chit, 91) - 1 (0, 1, 1, 3, 3, 4, 4)
Current Situation
N/D '40 Impulse 5 (Axis 2nd impulse), Air Rebase
Ge/It Entry Pool = 1, 1, 1, 1, 2, 3, 3, 5
Ge/It Tension Pool = 2, 2, 4, 4, 4, 4
Ja Entry Pool = 0, 1, 1, 3, 3, 4, 4
Ja Tension Pool = 1, 1, 1, 4, 4

Always listen to experts. They'll tell you what can't be done and why. Then do it!
-Lazarus Long, RAH