Peak output current of a Full-Wave Bridge Peak Rectifier
spice will be using a diode "model".  That model is likely to include things like recovery time and V-I curves.

The model may have a number of different break points that reflect the V-I curve of the real device.  Have a look at the data sheet of the device and you will find the V-I characteristic curves.  The forward drop will be found based on the current passing through the device and may not be exactly 0.7 V.

Also the recovery time of the diode may be having an impact in your spice model that is not shown in your equations.  Time taken for the diode to start conducting fully will allow some charge to pass through to the capacitor, hence reducing the peak current.

Try creating a perfect diode model that has a vertical V-I characteristic at 0.7 V and nothing else and compare that answer to your equations.

I would be happy using the theoretical value 855 mA in sizing the diodes for peak forward current as it is above the spice simulation.

Finally real life will be different again!  You will not have a capacitor as precise as 270.8 uF, a real capacitor will have ESR, a real transformer with have DC resistance, real components will heat up and there characteristic will change with temperature.