It does indeed seem strange, thankyou for sharing it with us. Unfortunately we don't have a magic crystal ball to magically see what your circuitry consists of.

If I understand correctly, you have a hall effect sensor connected to the adc0804. The hall effect sensor senses the current on the primary of a high frequency transformer. When you connect the hall effect sensor, weird things happen. Well, my mystical powers are working overtime tonight - I sense high currents at high frequencies - this tells me that stray pickup is most likely. This can be proven by moving the hall effect sensor to measure another lower current and frequency signal like the mains. If this works then we can say the problem is most likely stray pickup. How do we solve this? Keep your hall effect signal wires away and at right angles to the primary wire. Use shielded cable. Earth the shield. Put some low pass filtering on the input to your electronics. Then things might just start to work better.

Whilst the effect changed the operation of the EOC signal - that was not your problem. Changing the adc chip pretty well proved that. You chose to ignore the basics and you're paying for it! I think it was Ampere and Faraday that figured out the basics of electromagnetism many years ago and they didn't have an adc to measure the effect.