With my build, not using anteater but the hydraulic circuits still work similarly; my shift is initiated and I only have a delay of about 5mph at
WOT max. Hydraulically the shift from 2-3 for example, the pressure in the governor circuit overcomes the spring on shift spool valve and possibly whatever TV pressure is on the back side of that valve (that should be pretty instantaneous) and then the circuit fills to actuate the front band servo and direct drum piston. There may be a slight delay here, but I really don't think it should be anything like you are seeing.
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49 Willys Pickup. 5600lb. 11.8sec @115mph 1/4. 12 valve. MegaSquirted 47RH. 3.54 posi rear. 35" tires. 64mm HE351ve, S475 (75/96/1.32), A/W Intercooler. AFC mods. 5x16s. 191 DVs, 180 pump. 23*. 85psi.
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