Something along the lines of this: https://medium.com/coinmonks/how-to-implement-gas-less-transactions-on-ethereum-9f9273d2f059
Let's say the user has 1000 DAI and they want to convert 100 DAI into ETH over 10 weeks, they could presign all these transactions and give them to anyone for relaying.
For the sake of the hackathon we can just make a mock relayer that blindly submits user's presigned transaction payloads