I hear ya, these problems are a pain! Slow, detailed, meticulous testing is key to solution.
Is 86 a good ground? Have you checked to make sure?
Check resistance on BE/GY 30 from ecm to relay and from ecm fuse to ecm. See if that wire is shorting to ground. Also, capture live voltage on that wire while running up until the voltage goes crazy. Just make sure you don't feed current to ecu by mistake.
Somewhere in between the current is going high just like the code is suggesting. I assume it's shorting to ground as it warms up.
I believe the coil is on same circuit, test those wires as well. The coil could be shorting as it gets warm due to faulty lamination inside coil. I don't believe there is a fly back diode on that circuit to protect injectors. Oftentimes, they forget diode and figure relay will protect circuit. Not true...