How to add tiny 0.5A 120V load to very remote split phase 240v 3 wire well house
At 0.15A x 120V, this thing is about 18 VA (similar to watts).   That is significantly less than 40 VA.  

As it happens, 40VA thermostat transformers are cheap and common as dirt, typically around $13. They make them with both 240V and 120V primaries. Get one of each. 

You connect the two 24V secondaries to each other.  The 240V primary goes to the 240V main via a 1 amp fuse.  The 120V primary feeds your controller.   This is double-isolated from 240V, so it won't be terribly dangerous.  

If you really want to, you can call it a separately derived service and add a neutral-ground equipotential bond to whichever leg of the 120V you want to call "neutral", but given that it is going straight into another transformer that will also isolate it, that seems like much ado about nothing.  

I recommend to snip the plug off the cord and hardwire this thing, to avoid the temptation of someone plugging a circular saw into the outlet. 

Wow, that was easy and cheap.