How to design a load
AFAICT you will get what you want by using a shunt regulator:







simulate this circuit &ndash; Schematic created using CircuitLab

A shunt regulator works by drawing more current from the input supply if the load does not need that current. So it's easy to ensure a minimum load on the input. The current is set by (Vin-Vreg)/R1. You'd choose R1 based on the minimum input voltage to ensure your minimum load current.

You would do this separately for each of your inputs rather than for all 4 at once.

This solution also saves you having to find a giant capacitor to absorb 1 A while you're waiting for the load to kick in.

If the input voltage rises to 14.5 V, the shunt will sink more current; 1.3 A for the circuit I drew.

Finding (or designing) a shunt regulator able to sink 1-2 A is left as an excercise for the reader.