Converting a 4 to 20 mA signal to 0 to 5V
R4 and R5 are another load in parallel with your R6 in the top diagram, reducing the total load on the 4-20 signal to 118 ohms.  That is a problem.
Before you play with subtracting 1V from the overall output, buffer your 4-20mA signal through an op-amp to get the 1-5V signal, then you can perform additional operations on that.

One thing, be aware that the floor value (whatever voltage you get at 4mA) is often used to determine if the loop is broken or the transmitter has failed.  By normalizing things, your floor value will go negative in that case, which could be a problem downstream.