If you are TRULY working to a deadline how about offering a bonus for. Or simply put that in the job spec.
I NEED THIS DONE BY FRIDAY. iF YOU CAN'T DO THAT PLEASE DON'T WASTE MY TIME WITH USELESS BIDS!!!!!
Simply award the project. Make sure you have milestone payments. Failing compliance by the Conteactor, cancel the project. Don't make the milestone payment, then move on.
When you expect to get good work done cheap, you must factor in that the project will not get done. Itf you can't afford the time to do that then make two awards, Surely one will come through!
In the real world tier one contractors like IBM, et al deliver projects on budget, on time only 20% pf the time and that's in a good year. And they charge full rates! And their lawyers make sure they get paid for scope changes. In fact that is where tier one suppliers make their profits!
Remember the **Edited for Community Guidelines**