You don't even need to use points to get a super subsidised cheap hotel if you have a connecting QR ticket. And some hotels will comp their shuttle too if you are nice about it. But yes, the taxis and metro are very cheap anyway.

The best advice having already chosen the cheap long transfer itinerary to save yourself money, is to book the heavily subsidised hotel, enjoy an evening in Doha, sleep well, and then enjoy breakfast in the airside lounge if you want it, before then enjoying your long flight home. Easy. Especially when you have also saved up to $980 in the process.