Billiger-Mietwagen.de is usually my favorite for any car rental.
But they can't do wonder. Rent in France (or Germany) if you're after massive discounts. For a similar period as you're renting, I've had the model I needed for 500€ less renting in France vs. Switzerland. And it even had a Swiss Highway sticker applied
1 minute is already enough to get a huge fine that will prevent you from sleeping that night if you have not declared the car properly at the border. It is not allowed to rent/borrow a foreign car and drive it in Switzerland without the proper paper work. An exception for a few days can be arranged at the border for rentals, but OP needs the car for 16 days, so that is a no go.
There is not one company who is always cheapest, just compare the offerings. And play some with the dates, I've had cars that I chose to rent for 6 days since that gave me a lower price than only renting it for the needed 5 days.
And also have a good look on how many kilometers are included, and what the price is per extra kilometer. If you drive a lot often better to pay 100,- more for a car with unlimited kilometers. Also don't wait weeks with booking, prices often only go up the closer you get to the rental date.
Thanks. Just learned it's maximum 8 days apparently, and costs 20 CHF from using Google. Couldn't believe it's actually forbidden for a Swiss resident to drive a properly rented car into Switzerland without registering (and paying) for it, and even then just for a short period.
In my opinion, that's a more than just crazy piece of "law".
If I understand it correctly, if my French friend drops over the border, has one too many, I can't legally drive him in his own car back to the hotel?
Well, this isn't just Swiss. It's same in Poland (where I'm from), also in Austria (there was a loud case when a father - Austrian - of Swiss resident borrowed her car - Swiss registered - and tried to cross to Austria without doing any paperwork and got fined some ridiculous fine that was X times VAT due on that car... I think it was a fancy Merc)