If a site has a small 1ph supply, then my advice was always to run all long-duration kit like lights, & all small power tools off 1ph.I used to do a bit in a yard that was solely powered by a 40 kVa diesel set and always a ballache to keep the diesel tank full etc and even in relatively good order and in a manufacturer's acoustic canopy, you got fed up with its background noise so much so that we would turn it off at lunch break. Recently the alternator failed and very expensive to replace so much so that the set will probably be sold for export as is and replaced. In the long run, mains elec would have been cheaper even with the large initial cost. Always worried about the engine operating at low load for too many hours as often just powering just lights and a few hand tools. There's a large three phase welding set there and you can definitely hear the engine govern-up when you strike an arc and I'm sure this helped to save the engine from glazing up .
Keep the genny on a remote-start, & only use it for the essential 3ph loads.
If the genny needs to run a process for a longer continuous period, then you can fit a changeover switch (or even IEE plug socket system) to add the 1ph loads onto the genny during the run, then revert back to mains 1ph when the 3ph is not needed.