Why does introducing the fuel at lower speed produce higher EGT's?
Because as stated earlier
The thing is jets are air cooled so you need to pump air in to cool them
Not enough air to cool while combustion is taking place causing a rise in EGT. Air going to the combuster after passing through the compressor core is used in different ways, some is mixed with the fuel and burnt some is used to position the flame and some is used for cooling the combuster case, with not enough air, although the fuel will burn the flame is not positioned right and the combuster case losses the cooling effect from the cooling air causing an increased temp exiting the combustor to the turbine which is getting cooked as the turbine section has less cooling air causing the indication to pick up the increased EGT.