Fruit – thesterious green middle eastern plums

Like many fruits and vegetables, the sugar level in a plantain increases as it ripens.

• Green plantains are very starchy and hard. You must cook them to eat them. They can be used much like a potato (think chopped & put in soups or mashed as a side dish). Fried green plantains are referred to as "tostones."
• Yellow plantains still require cooking, but they are sweet (unlike green plantains). These work pretty well for frying and steaming.
• Black (super-ripe) plantains do not have to be cooked; they can be eaten raw. They have soft flesh and a scent like a banana, though still not as sweet as typical bananas. When these super-ripe plantains are fried, they are referred to as "platanos maduros" (ripe plantains) or "platanos fritos" (fried plantains).

Regarding use by different cultures:

Trinidad and Tobago, Honduras and Jamaica: the plantain is either simply fried, boiled or added to a soup.
Kerala: ripe plantain is steamed and is a popular breakfast dish.
Ghana: boiled plantain is eaten with kontomire stew, cabbage stew or fante-fante (fish) stew. The boiled plaintain can be mixed with groundnut paste, pepper, onion and palm oil to make eto, which is eaten with avocado.
Southern United States, particularly in Texas, Louisiana and Florida: plantains are most often grilled.
Nigeria: plantain is eaten boiled, fried or roasted; roasted plantain, called booli is usually eaten with palm oil or groundnut.
(source)

I think freezing would be your best bet - not fantastic for the texture, but when defrosted you could make a pie/cobbler or other cooked item with them. Plenty of web sites (eg http://www.fruitexpert.co.uk/using-up-a-plum-glut.html) say you can just halve them and freeze them on open tray, then when they're frozen move them into plastic bags. It's the lowest-effort option so probably worth trying on at least a fraction of your harvest.