how would the circuit look like?
Sorry, I did not look at the schematic at first.
When having a lower voltage to override a higher one, things get a bit more complicated.
The or-ing with diodes is only usefull to select the higest voltage of the two, and the relay only
bypasses the diode to eliminate the forward voltage drop.
In this case you could use two back-to-back P-Mosfets two disable the battery (sources & gates together),
but with limited electronic experience, you're probably better of using a capacitor;
dV/dt=i/C or C=I*dt/dV
dV=4V (12Vtyp-8Vmin), dt=10msec, I=5A, then C=12500uF.
Quite large indeed, but not excessive. With a bit of luck, you can get away with 10mF/16V, which are about 25x25mm in size.
Btw you might want to change the series diodes to an anti-parallel configuration and a fuse. The diodes eat some 1volt=5watts away, which is a waste and also reduces the headroom voor voltage dips.