The diodes for the current protection need to be quite beefy, as they have to carry the current needed to blow the fuse. So they should stand something like 1.5 times the fuse rating with sufficient peak rating. So the obvious choice are slow rectifier diodes.
The forward drop on the S3M looks relatively high though. So the shunts may worst case see quite some power.
With bootstrapping the diodes one might consider using only 1 diode. However this might start to limit peaks in AC current.
Having the diodes close together with not much cooling is a good thing as this lowers the drop when the diodes get warm.
The diodes to protect the AC amplifier should be smaller to avoid the high capacitance. So more like a 1N4148 or BAV199. That is definitely a point to change.
One could check the effect of the relay getting warm by looking at the offset in the current ranges. Ideally there would be essentially no current measured with open terminal. Thermal EMF can introduce an offset of a few µV that could be visible as some zero error in the current.
p.S: the lower shunts also look rather small form factor. So they may show quite some self heating effect with higher current. 2 A at 200 mV burden gives 400 mW power loss. This normally calls for a resistor that is more like 5 W normal power rating. The power rating of SMD parts is valid on a massive copper plane board not the more practical layouts
. Also a symmetric thermal layout around that resistor could help to avoid errors.