Dont think a a 310 or a Baron will carry 650Kg, though I dont know the rules in the phillipines but if they want you to stick to the POH I think you will be out of luck!
The PA31 will, as for short field performance though I'd have to say its crap in the tropics. Haven't flown the aerocommader but would say it would be definitely worth a look as from what I know it can match the PA31 and prob have better field performance.
Good Luck.
forgot to mention that if a lighter weight is acceptable more like 450kg then 310 is ok on rough airstrips, but would be no different to a baron. 310's(unless a gear mod has been done) can be prone to a main gear collapse though.