Inverters are not 100% efficient. They get more efficient as they reach their max output so you should size your inverters with care if pinching every last watt is important to you (as it is for me). More electronic cut outs and sensors and whatnot are just going to be more electrical draws.
Solar living has three main components:
1. lower your power consumption
2. increase your power production
3. increase your power storage.
for your fridge, I wouldn't complicate things with relays and voltage sensors and automatic cut outs. Increase the efficiency of the fridge with better and more insulation while making sure that the fridge can dump out the heat it makes through the coils on the back. Put your fridge on a timer so it only comes on during daylight (charging) hours and don't open the door outside of those times.
If batteries are unaffordable, lower your standards and run the batteries that someone else thought no good anymore and test them frequently. Keep the ones that work well, recycle the others. 'They' say that batteries are only good for a short number of years but this is not really true. With care a good battery can last as long as twenty years without too much loss of overall capacity. More importantly, a battery that is only holding 3/4 of it's original capacity is still a viable battery and rich folks will throw them away as soon as they are no longer 'perfect'. You will still get some valuable use out of them.