I was doing some research on hammurabi and I got a much earlier date then I am used to on him:

First Babylonian Dynasty:

1959-1945 Su-abu or Suum-abum
1945-1909 Sumula-ilum
1909-1895 Sabium or Sabum
1895-1877 Apil-Sin
1877-1857 Sin-muballit
1857-1814 Hammurabi

Now this would correspond with Senwosret III in egypt is it possible that these are the same person considering you said that amenemhet IV is the pharoah of this exodus? Alot of people break hammurabi down like a mmu rabi saying he was an amor-ite but I have also seen his name spelled khammurabi could it be kham ur abi? Here is why I asked; I looked at both of the busts of senusret III and Hammurabi and if you take the beard off of Hammurabi it is very interesting:

Senusret III


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Hammurabi and Senusret III