The batteries could be the problem. The spike you're seeing is the change in charging current (when load is disconnected), multiplied by the internal resistance of the batteries. The greater the resistance, the larger the "spike".
If the batteries were low on water then they could be sulfated. The more they get sulfated, the greater the battery resistance becomes, resulting in bigger "spikes".
Your batteries are small to begin with. This means they already have an inherent larger resistance. You can get a measure of resistance without an amp meter. With solar charging, and battery around 14.4V, toggle your load that you normally use. Measure volts directly at batteries immediately before and after removing the load. We're interested in the voltage difference between the two measurements. Do this 5 or 6 times to get a consistent measurement. What's the estimated load current you are toggling?
Sal
