How to increase hall sensor voltage
Figure 1. Small loads can be driven directly by the Hall sensor's NPN output.

Where currents higher than the 10 mA rating of the sensor then use one of the schemes shown on page 2 of the datasheet.



Figure 2. (Top) External NPN inverting switch. (Bottom) External PNP non-inverting switch.


The upper circuit will be normally on due to the bias provided to the NPN transistor by the 1.2k resistor. When the Hall sensor turns on its output will pull low and steal the bias from the transistor so the load will turn off.
The lower circuit is off by default. When the Hall sensor switches low it will pull current from the base of the PNP transistor and turn it on.



  ... but only puts out 380-400mv on the supply line ...


No, that specification means that it can pull the output down to 380 - 400 mV (capital V for volt) when it is turned on. This is important in the upper circuit as we need to pull lower than about 0.6 V to turn off the NPN transistor.

The Crydom SSR is a little more sophisticated than my Figure 1 suggests. Rather than a series resistor on the input side it probably has a constant current circuit to drive the required current (probably about 10 mA) through the internal LED. The datasheet should give the actual value.