Unexpected results in voltage to current converter (simulation is Ok)
It is certainly unusual and suggests your high side analog switches are high impedance. Check that they have adequate gate voltage.   Try CD4066's or similar for your experiment.
Reality is complex since the schematic does not show all the stray capacitance and protection diodes and unexpected results occur.

The switches complement the polarity of current to the load but then go to Tristate (unknown charge voltage)  This does not seem practical and is neither a Sample and hold, nor a switch capacitor design, but something that does not behave properly with high impedance charges.