Irregular shapes are always tricky, yet bin bags generally give the capacity in litres plus the dimensions. Might that be a way to guestimate this?
Take some small bin bags (compost ones?), blow them up with air, close them and see how many it takes to fill them?
As already said, water-filling requires a very strong bag. Air-filling would not but air is harder to measure (remember 1 litre of water is 1kg (at 4°C etc.)).
Submersing the bag to see the amount of water it can be displace requires some very big water containers and since we are talking about displacing ~270 litres there would still be a lot of force involved. However displacement & submersion has the advantage that it can work gradually so as long as the bag was airtight enough the full 270kg of displaced water would never have to be applied all at once, but at the end you are still displacing 270kg which is asking a lot (too much) from a plastic bag.
Guess if you wanted to measure a balloon you'd make a cast and burst the balloon. A lot of work but probably the most accurate thing to do.