How to convert output from a split phase inverter to single phase with only 1 hot?
Philippine power (in the American zones) is a worldwide one-off: it is simply North American style power, but with neutral omitted.   Safety ground is still there, but it's halfway between the hots.   

Indeed, any Philippine appliance can come to the US, be plugged into a properly wired NEMA 6, and be happy as a clam. 

In the Euro-power zones of the Philippines, it's the same except safety ground is pegged to one of the poles instead of halfway in between.  In other words, bog-standard 5-continent power. 

So, to make your inverter work with the Philippines, where you would normally provide a standard NEMA 14 receptacle, instead, provide NEMA 6 and don't serve neutral.  

Although truth be told, even though the NEMA connector system provides the correct socket for this (NEMA 6), my understanding is that in practice, the Philippines prefer NEMA 5 even though it's wrong.  (what are they thinking?)  

I wouldn't say things made for 220V "work even better" on 240V.  However, I would say that anything made 220/240 for the North American market, will be built for 240V.  Also, anything built for the Euro/5-continent market will at least be built for 230V as that is the Euro standard, and maybe even 240V since that is the British standard.