Cook with no hood - how to control smell
Is there a bathroom with a fan? Setting up a portable electric hob just outside the bathroom with the door open might help, especially if you can also leave the front door ajar during cooking to provide a through-draught. You could use a folding table if the existing furniture isn't sufficient. 

Covering as much as possible, choosing thing with short cooking times, and clearing up promptly will all help a bit, but won't make the problem go away. Low fat approaches are very suitable as frying causes a lot of odour compared to simmering. The low sodium approach cuts out a lot of prepared sauces, which would mean more cooking of flavour ingredients like onions or spices. 

A camping stove on top of the BBQ would give you a few more options, but still relies on having good enough weather to cook outside. Compared to the BBQ it gets going quicker and it's better for all wet forms of cooking.